universal mechanism for the intermittent route to strange nonchaotic attractors in quasiperiodically forced systems to examine the universality for the intermittent route to strange nonchaotic attractors snas we investigate the quasiperiodically forced henon map ring map and toda oscillator which are high dimensional invertible systems in these invertible systems dynamical transition to an intermittent sna occurs via a phase dependent saddle node bifurcation when a smooth torus collides with a ring shaped unstable set we note that this bifurcation mechanism for the appearance of intermittent snas is the same as that found in a simple system of the quasiperiodically forced noninvertible logistic map hence the intermittent route to snas seems to be universal in the sense that it occurs through the same mechanism in typical quasiperiodically forced systems of different nature

self dual solutions to pseudo yang mills equations abstract we study pseudo yang mills fields on a compact 5 dimensional strictly pseudoconvex cr manifold m i e critical points to the functional y m b d 1 2 m h r d 2 d 2 on the space c e h of all connections d on a hermitian vector bundle e h over m such that d h 0 if a d c e h r d 0 g tr r d d 0 and d a is an absolute minimum to y m b a r then i b tr r d 0 and ii d is self dual or anti self dual according to the sign of c 2 d m p 2 d m 1 2 m p 1 d p 1 d where p k d is the k th chern form of e d and provided c 2 d is constant on a

strange nonchaotic attractors with wada basins a b s t r a c t we demonstrate strange nonchaotic attractors with wada basins snaswb and verify the abundance of snaswb in a quasiperiodically forced holmes map we identify the routes to the creation of the snaswb in a two parameter space the snaswb are characterized by the maximal lyapunov exponent by the estimation of the phase sensitivity exponent and by the singular continuous spectra we observe that the snas basins are totally wada basins in a large range of parameters the topological structures of the snas wada basins are distinguished by the basin cell method we investigate the underlying mechanism for the abundance of snaswb which is responsible for different types of basin cell in the absence of forcing this suggests that the snas cannot be predicted reliably for specific initial conditions these snaswb can thus be expected to occur more commonly in dynamical systems

asymptotics of complete kahler metrics of finite volume on quasiprojective manifolds let x be a quasiprojective manifold given by the complement of a divisor d with normal crossings in a smooth projective manifold x using a natural compactification of x by a manifold with corners x we describe the full asymptotic behavior at infinity of certain complete kahler metrics of finite volume on x when these metrics evolve according to the ricci flow we prove that such asymptotic behaviors persist at later times by showing that the associated potential function is smooth up to the boundary on the compactification x however when the divisor d is smooth with kx d 0 so that the ricci flow converges to a kahler einstein metric we show that this kahler einstein metric has a rather different asymptotic behavior at infinity since its associated potential function is polyhomogeneous with in general some logarithmic terms occurring in its expansion at the boundary

fractal basin boundaries abstract basin boundaries for dynamical systems can be either smooth or fractal this paper investigates fractal basin boundaries one practical consequence of such boundaries is that they can lead to great difficulty in predicting to which attractor a system eventually goes the structure of fractal basin boundaries can be classified as being either locally connected or locally disconnected examples and discussion of both types of structures are given and it appears that fractal basin boundaries should be common in typical dynamical systems lyapunov numbers and the dimension for the measure generated by inverse orbits are also discussed

the classical schrodinger equation prufer s spectral algorithm is applied to the classical analogue of schrodinger s equation the discrete spectrum is interpreted as a bifurcation phenomenon caused by two simultaneous classical motions rotation and squeezing the energy eigenvalues coincide with the bifurcation parameters for the classical orbits

incidence of nonextensive thermodynamics in temporal scaling at feigenbaum points abstract recently in phys rev lett 95 2005 140601 grassberger addresses the interesting issue of the applicability of q statistics to the renowned feigenbaum attractor he concludes there is no genuine connection between the dynamics at the critical attractor and the generalized statistics and argues against its usefulness and correctness yet several points are not in line with our current knowledge nor are his interpretations we refer here only to the dynamics on the attractor to point out that a correct reading of recent developments invalidates his basic claim

pseudo einstein structures on cr manifolds etant donne une variete cr compacte non degeneree on cherche une structure pseudohermitienne associee pour laquelle le tenseur de ricci pseudohermitien est un multiple scalaire de la forme de levi

localizations on complex networks we study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix the probability distribution function of the components of the representative eigenvectors are proposed to describe the localization on networks where the euclidean distance is invalid several quantities are used to describe the localization properties of the representative states such as the participation ratio the structural entropy and the probability distribution function of the nearest neighbor level spacings for spectra of complex networks whole cell networks in the real world and the watts strogatz small world and barabasi albert scale free networks are considered the networks have nontrivial localization properties due to the nontrivial topological structures it is found that the ascending order ranked series of the occurrence probabilities at the nodes behave generally multifractally this characteristic can be used as a structural measure of complex networks

renormalization of correlations in a quasiperiodically forced two level system quadratic irrationals generalizing from the case of golden mean frequency to a wider class of quadratic irrationals we extend our renormalization analysis of the self similarity of correlation functions in a quasiperiodically forced two level system we give a description of all piecewise constant periodic orbits of an additive functional recurrence generalizing that present in the golden mean case we establish a criterion for periodic orbits to be globally bounded and also calculate the asymptotic height of the main peaks in the correlation function

universal criterion for the breakup of invariant tori in dissipative systems the transition from quasiperiodicity to chaos is studied in a two dimensional dissipative map with the inverse golden mean rotation number on the basis of a decimation scheme it is argued that the minimal slope of the critical iterated circle map is proportional to the effective jacobian determinant approaching the zero jacobian determinant limit the factor of proportion becomes a universal constant numerical investigation on the dissipative standard map suggests that this universal number could become observable in experiments

tsallis q index and mori s q phase transitions at the edge of chaos we uncover the basis for the validity of the tsallis statistics at the onset of chaos in logistic maps the dynamics within the critical attractor is found to consist of an infinite family of mori s q phase transitions of rapidly decreasing strength each associated with a discontinuity in feigenbaum s trajectory scaling function sigma the value of q at each transition corresponds to the same special value for the entropic index q such that the resultant sets of q lyapunov coefficients are equal to the tsallis rates of entropy evolution

temporal scaling at feigenbaum points and nonextensive thermodynamics we show that recent claims for the nonstationary behavior of the logistic map at the feigenbaum point based on nonextensive thermodynamics are either incorrect or can be easily deduced from well known properties of the feigenbaum attractor in particular there is no generalized pesin identity for this system the existing attempts at proofs being based on misconceptions about basic notions of ergodic theory in deriving several new scaling laws of the feigenbaum attractor thorough use is made of its detailed structure but there is no obvious connection to nonextensive thermodynamics

criticality in nonlinear one dimensional maps rg universal map and nonextensive entropy abstract we consider the period doubling and intermittency transitions in iterated nonlinear one dimensional maps to corroborate unambiguously the validity of tsallis nonextensive statistics at these critical points we study the map x n 1 x n u x n z z 1 as it describes generically the neighborhood of all of these transitions the exact renormalization group rg fixed point map and perturbation static expressions match the corresponding expressions for the dynamics of iterates the time evolution is universal in the rg sense and the nonextensive entropy s q associated to the fixed point map is maximum with respect to that of the other maps in its basin of attraction the degree of nonextensivity the index q in s q and the degree of nonlinearity z are equivalent and the generalized lyapunov exponent q q 2 q 1 is the leading map expansion coefficient u the corresponding deterministic diffusion problem is similarly interpreted we discuss our results

boundary behaviors for liouville s equation in planar singular domains abstract we study asymptotic behaviors near the boundary of complete metrics of constant curvature in planar singular domains and establish an optimal estimate of these metrics by the corresponding metrics in tangent cones near isolated singular points on boundary the conformal structure plays an essential role

normal mode analysis of spectra of random networks abstract several spectral fluctuation measures of random matrix theory rmt have been applied in the study of spectral properties of networks however the calculation of those statistics requires performing an unfolding procedure which may not be an easy task in this work network spectra are interpreted as time series and we show how their short and long range correlations can be characterized without implementing any previous unfolding in particular we consider three different representations of erd s renyi er random networks standard er networks er networks with random weighted self edges and fully random weighted er networks in each case we apply singular value decomposition svd such that the spectra are decomposed in trend and fluctuation normal modes we obtain that the fluctuation modes exhibit a clear crossover between the poisson and the gaussian orthogonal ensemble statistics when the average degree of er networks changes moreover by using the trend modes we perform a data adaptive unfolding to calculate for comparison purposes traditional fluctuation measures such as the nearest neighbor spacing distribution number variance 2 as well as 3 and n statistics the thorough comparison of rmt short and long range correlation measures make us identify the svd method as a robust tool for characterizing random network spectra

renormalization analysis of correlation properties in a quasiperiodically forced two level system we give a rigorous renormalization analysis of the self similarity of correlation functions in a quasiperiodically forced two level system more precisely the system considered is a quantum two level system in a time dependent field consisting of periodic kicks with amplitude given by a discontinuous modulation function driven in a quasiperiodic manner at golden mean frequency mathematically our analysis consists of a description of all piecewise constant periodic orbits of an additive functional recurrence we further establish a criterion for such orbits to be globally bounded functions in a particular example previously only treated numerically we further calculate explicitly the asymptotic height of the main peaks in the correlation function

bubbling route to strange nonchaotic attractor in a nonlinear series lcr circuit with a nonsinusoidal force we identify an unconventional route to the creation of a strange nonchaotic attractor sna in a quasiperiodically forced electronic circuit with a nonsinusoidal square wave force as one of the quasiperiodic forces through numerical and experimental studies we find that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square wave type force the bubbles then enlarge and get increasingly wrinkled as a function of the control parameter finally the bubbles get extremely wrinkled while the remaining parts of the strands of the torus remain largely unaffected resulting in the creation of the sna we term this the bubbling route to the sna we characterize and confirm this creation from both experimental and numerical data using maximal lyapunov exponents and their variance poincar e maps fourier amplitude spectra and spectral distribution functions we also strongly confirm the creation of a sna via the bubbling route by the distribution of the finite time lyapunov exponents

boundary behavior of harmonic functions in metrics of bergman type on the polydisc in this paper we prove the following theorem any harmonic functions in bergman type metrics in the polydisc in complex euclidean space which are continuous up to the boundary must be harmonic in each complex variable

equivalence between the mobility edge of electronic transport on disorderless networks and the onset of chaos via intermittency in deterministic maps we exhibit a remarkable equivalence between the dynamics of an intermittent nonlinear map and the electronic transport properties obtained via the scattering matrix of a crystal defined on a double cayley tree this strict analogy reveals in detail the nature of the mobility edge normally studied near not at the metal insulator transition in electronic systems we provide an analytical expression for the conductance as a function of the system size that at the transition obeys a q exponential form this manifests as power law decay or few and far between large spike oscillations according to different kinds of boundary conditions

boundary behavior of large solutions to the monge ampere equations with weights abstract this paper is concerned with the monge ampere equation det d 2 u x b x f u x x where is a strictly convex bounded smooth domain in r n with n 2 and b c which is positive in but may be vanishing on the boundary we find a new structure condition on f which plays a crucial role in the boundary behavior of strictly convex large solutions our results are obtained in a more general setting than those in cirstea and trombetti 2008 12 where f is regularly varying at infinity with index p n

uniqueness and regularity of proper harmonic maps introduction the purpose of this paper is to study some uniqueness and regularity properties of the dirichlet problem at infinity for proper harmonic maps between hyperbolic spaces in general if the metrics of two complete noncompact manifolds mm and n are given locally by ds2 imj gij dxzdxj and dsy en h 3 du du respectively then the energy density function of a c1 map u m n is defined by

harper equation the dissipative standard map and strange nonchaotic attractors relationship between an eigenvalue problem and iterated maps the almost periodic eigenvalue problem described by the harper equation is connected to other classes of quasiperiodic behavior the dissipative dynamics on critical invariant tori and quasiperiodically driven maps firstly the strong coupling limit of the supercritical harper equation and the strong dissipation limit of the critical standard map play equivalent role in describing the universal characteristics of these systems secondly a simple transformation is used to relate the harper equation to a quasiperiodically forced one dimensional map in this case the localized eigenstates of the supercritical harper equation correspond to strange but nonchaotic attractors of the driven map furthermore the existence of localization in the eigenvalue problem is associated with the appearance of homoclinic points in the corresponding map

the renormalization group and optimization of non extensive entropy criticality in non linear one dimensional maps abstract we examine the pitchfork and tangent bifurcations in unimodal maps to illustrate a connection between renormalization group rg fixed points and entropy extremal properties we observe that the exact rg solution for the tangent bifurcation is also applicable to the period doubling cascade and assess its physical meaning since the expression for the fixed point map can be put into the form of the non extensive expressions for the temporal evolution of phase space volume and sensitivity of initial conditions we conclude that the map critical points possess the properties of this formalism the universality of the rg solution makes this interpretation inclusive to all one dimensional maps of non linearity z 1

an extension problem for the cr fractional laplacian we show that the conformally invariant fractional powers of the sub laplacian on the heisenberg group are given in terms of the scattering operator for an extension problem to the siegel upper halfspace remarkably this extension problem is different from the one studied among others by caffarelli and silvestre we also prove an energy identity that yields a sharp trace sobolev embedding

universal properties of the transition from quasi periodicity to chaos in dissipative systems abstract an exact renormalization group transformation is developed for dissipative systems which describes how the transition to chaos may occur in a continuous and universal manner if the frequency ratio in the quasi periodic regime is held at a fixed irrational value our approach is a natural extension of k a m theory to strong coupling most of our analysis is for analytic circle maps we have found a strong coupling fixed point where invertibility is lost which describes the universal features of the transition to chaos we find numerically that any two such critical maps with the same winding number are c 1 conjugate it follows that the low frequency peaks in an experimental spectrum are universal and we determine how their envelope scales with frequency when the winding number has a periodic continued fraction our renormalization transform has a fixed point and spectra are self similar in addition for a set of non periodic winding numbers with full measure our renormalization transformation yields an ergodic trajectory in a sub space of all critical maps physically one finds singular and universal spectra that do not scale

the birth of strange nonchaotic attractors abstract a mechanism is described for the development of strange nonchaotic attractors from two frequency quasiperiodic attractors in quasiperiodically driven maps this mechanism is intimately tied to the phenomenon of torus doubling the transition to strange nonchaotic behavior occurs when a period doubled torus collides with its unstable parent torus as the collision is approached the period doubled torus becomes extremely wrinkled ultimately becoming fractal at the collision the lyapunov exponent remains negative through the collision these collisions are shown to be a new type of attractor merging crisis the new feature is the possibility of nonchaotic attractors taking part in the crisis this mechanism is illustrated via numerical and analytical studies of a quasiperiodically driven logistic map

quasiperiodicity in dissipative systems a renormalization group analysis abstract dynamical systems with quasiperiodic behavior i e two incommensurate frequencies may be studied via discrete maps which show smooth continuous invariant curves with irrational winding number in this paper these curves are followed using renormalization group techniques which are applied to a one dimensional system circle and also to an area contracting map of an annulus two fixed points are found representing different types of universal behavior a trivial fixed point for smooth motion and a nontrivial fixed point the latter representsthe incipient breakup of a quasiperiodic motion with frequency ratio the golden mean into a more chaotic flow fixed point functions are determined numerically and via an e expansion and eigenvalues are calculated

renormalization of correlations and spectra of a strange non chaotic attractor we study a simple nonlinear mapping with a strange nonchaotic attractor characterized by a singular continuous power spectrum we show that the symbolic dynamics is exactly described by a language generated from a suitable inflation rule we derive renormalization transformations for both the power spectrum and the autocorrelation function thus obtaining a quantitative description of the scaling properties the multifractal nature of the spectrum is also discussed

polynomial approximation local polynomial convexity and degenerate cr singularities abstract we begin with the following question given a closed disc d c and a complex valued function f c d is the uniform algebra on d generated by z and f equal to c d when f c 1 d this question is complicated by the presence of points in the surface s graph d f that have complex tangents such points are called cr singularities let p s be a cr singularity at which the order of contact of the tangent plane with s is greater than 2 i e a degenerate cr singularity we provide sufficient conditions for s to be locally polynomially convex at the degenerate singularity p this is useful because it is essential to know whether s is locally polynomially convex at a cr singularity in order to answer the initial question to this end we also present a general theorem on the uniform algebra generated by z and f which we use in our investigations this result may be of independent interest because it is applicable even to non smooth complex valued f

a garden of orchids a generalized harper equation at quadratic irrational frequencies we consider a generalized harper equation at quadratic irrational flux showing in the strong coupling limit the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set this work generalizes previous analyses which have considered only the golden mean case projections of the renormalization strange sets are illustrated analogous to the orchid present in the golden mean case

closer look at time averages of the logistic map at the edge of chaos the probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown see u tirnakli c beck and c tsallis phys rev e 75 040106 r 2007 to be numerically consistent with a q gaussian the distribution which under appropriate constraints maximizes the nonadditive entropy sq the basis of nonextensive statistical mechanics this analysis was based on a study of the tails of the distribution we now check the entire distribution in particular its central part this is important in view of a recent q generalization of the central limit theorem which states that for certain classes of strongly correlated random variables the rescaled sum approaches a q gaussian limit distribution we numerically investigate for the logistic map with a parameter in a small vicinity of the critical point under which conditions there is convergence to a q gaussian both in the central region and in the tail region and find a scaling law involving the feigenbaum constant our results are consistent with a large number of already available analytical and numerical evidences that the edge of chaos is well described in terms of the entropy sq and its associated concepts

kahler einstein metrics with edge singularities this article considers the existence and regularity of kahler einstein metrics on a compact kahler manifold m with edge singularities with cone angle 2 along a smooth divisor d we prove existence of such metrics with negative zero and some positive cases for all cone angles 2 2 the results in the positive case parallel those in the smooth case we also establish that solutions of this problem are polyhomogeneous i e have a complete asymptotic expansion with smooth coecients along d for all 2 2

localization transition on complex networks via spectral statistics the spectral statistics of complex networks are numerically studied the features of the anderson metal insulator transition are found to be similar for a wide range of different networks a metal insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small the critical index of the transition corresponds to the mean field expectation when the connectivity is higher the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity though a precise transition cannot be identified the absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks resulting in a small diameter even for a large number of sites

equivalence among different formalisms in the tsallis entropy framework abstract in a recent paper t wada a m scarfone phys lett a 335 2005 351 the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the tsallis entropy framework in the present letter we extend these results to a system which is out of equilibrium and evolves to a stationary state according to a nonlinear fokker planck equation nfpe by means of time scale conversion it is shown that there exists a correspondence among the self similar solutions of the nfpes associated with the different tsallis formalisms the time scale conversion is related to the corresponding lyapunov functions of the respective nfpes

localization delocalization transition in hessian matrices of topologically disordered systems using the level spacing ls statistics we have investigated the localization delocalization transitions ldts in hessian matrices of a simple fluid with short ranged interactions the model fluid is a prototype of topologically disordered systems and its hessian matrices are recognized as an ensemble of euclidean random matrices with elements subject to several kinds of constraints two ldts in the hessian matrices are found with one in the positive eigenvalue branch and the other in the negative eigenvalue one the locations and the critical exponents of the two ldts are estimated by the finite size scaling for the second moments of the nearest neighbor ls distributions within numerical errors the two estimated critical exponents are almost coincident with each other and close to that of the anderson model am in three dimensions the nearest neighbor ls distribution at each ldt is examined to be in a good agreement with that of the am at the critical disorder we conclude that the ldts in the hessian matrices of topologically disordered systems exhibit the critical behaviors of orthogonal universality class

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

strange non chaotic attractor in a quasiperiodically forced circle map abstract we show that in the quasiperiodically forced circle map strange non chaotic attractors can appear for non linearities far from the border of chaos the destruction of a two frequency quasiperiodic torus connected with the appearance of a strange non chaotic attractor is described in detail this strange non chaotic attractor is characterized by logarithmically slow diffusion of the phase it is shown that in this regime the high order phase locking states disappear and the rotation number varies rather smoothly with the parameters

q deformed statistical mechanical property in the dynamics of trajectories en route to the feigenbaum attractor we demonstrate that the dynamics toward and within the feigenbaum attractor combine to form a q deformed statistical mechanical construction the rate at which ensemble trajectories converge to the attractor and to the repellor is described by a q entropy obtained from a partition function generated by summing distances between neighboring positions of the attractor the values of the q indices involved are given by the unimodal map universal constants while the thermodynamic structure is closely related to that formerly developed for multifractals as an essential component in our demonstration we expose in great detail the features of the dynamics of trajectories that either evolve toward the feigenbaum attractor or are captured by its matching repellor the dynamical properties of the family of periodic superstable cycles in unimodal maps are seen to be key ingredients for the comprehension of the discrete scale invariance features present at the period doubling transition to chaos elements in our analysis are the following i the preimages of the attractor and repellor of each of the supercycles appear entrenched into a fractal hierarchical structure of increasing complexity as period doubling develops ii the limiting form of this rank structure results in an infinite number of families of well defined phase space gaps in the positions of the feigenbaum attractor or of its repellor iii the gaps in each of these families can be ordered with decreasing width in accordance with power laws and are seen to appear sequentially in the dynamics generated by uniform distributions of initial conditions iv the power law with log periodic modulation associated with the rate of approach of trajectories toward the attractor and to the repellor is explained in terms of the progression of gap formation v the relationship between the law of rate of convergence to the attractor and the inexhaustible hierarchy feature of the preimage structure is elucidated vi a mean field evaluation of the atypical partition function a thermodynamic interpretation of the time evolution process and a crossover to ordinary exponential statistics are given we make clear the dynamical origin of the anomalous thermodynamic framework existing at the feigenbaum attractor

variations of kahler einstein metrics on strongly pseudoconvex domains let z s in mathbb c n times mathbb c m and pi mathbb c n times mathbb c m rightarrow mathbb c m be the projection on the second factor let d be a smooth domain in mathbb c n m such that for each s in pi d the n dimensional slice d s d cap pi 1 s z z s in d is a smooth bounded strongly pseudoconvex domain by a theorem of cheng and yau for each slice d s there exists a unique complete kahler einstein metric h alpha bar beta z s with a negative constant ricci curvature we prove that if the slice dimension n is greater than or equal to 3 then log det h alpha bar beta 1 le alpha beta le n is a plurisubharmonic function on d we also prove that it is a strictly plurisubharmonic function if d is a strongly pseudoconvex domain

construction of boundary invariants and the logarithmic singularity of the bergman kernel in which case the coefficients aj are expressed by the weyl invariant theory in terms of the riemannian curvature tensor and its covariant derivatives the bergman kernel s counterpart of the time variable t is a defining function r of the domain by f1 and bs the formal singularity of k at a boundary point p is uniquely determined by the taylor expansion of r at p thus one has hope of expressing modulo on 1 r and modulo o r in terms of local biholomorphic invariants of the boundary provided r is appropriately chosen in f3 fefferman proposed to find such expressions by reducing the problem to an algebraic one in invariant theory associated with cr geometry and indeed expressed modulo on 19 r invariantly by solving the reduced problem partially the solution in f3 was then completed in beg to give a full invariant expression of modulo on 1 r but the reduction is still

scattering and transport properties of tight binding random networks we study numerically scattering and transport statistical properties of tight binding random networks characterized by the number of nodes n and the average connectivity we use a scattering approach to electronic transport and concentrate on the case of a small number of single channel attached leads we observe a smooth crossover from insulating to metallic behavior in the average scattering matrix elements the conductance probability distribution w t the average conductance the shot noise power p and the elastic enhancement factor f by varying from small 0 to large 1 values we also show that all these quantities are invariant for fixed n moreover we proposes a heuristic and universal relation between and p and the disorder parameter

on the asymptotic expansion of complete ricciflat kahler metrics on quasi projective manifolds in this work we describe the asymptotic behavior of complete metrics with prescribed ricci curvature on open kahler manifolds that can be compactified by the addition of a smooth and ample divisor first we construct a explicit sequence of kahler metrics with special approximating properties using those metrics as starting point we are able to work out the asymptotic behavior of the solutions given in ty1 in particular obtaining their full asymptotic expansion

multifractality and nonextensivity at the edge of chaos of unimodal maps we examine both the dynamical and the multifractal properties at the chaos threshold of logistic maps with general nonlinearity z 1 first we determine analytically the sensitivity to initial conditions t then we consider a renormalization group operation on the partition function z of the multifractal attractor that eliminates one half of the multifractal points each time it is applied invariance of z fixes a length scale transformation factor 2 in terms of the generalized dimensions d there exists a gap in the values of equal to q 1 1 q d 1 d 1 where q is the q generalized lyapunov exponent and q is the nonextensive entropic index we provide an interpretation for this relationship previously derived by lyra and tsallis between dynamical and geometrical properties

quasiperiodically forced dynamical systems with strange nonchaotic attractors abstract we discuss the existence and properties of strange nonchaotic attractors of quasiperiodically forced nonlinear dynamical systems we do this by examining a particular model differential equation cos e cos 2 t where is a two frequency quasiperiodic function of t when 0 the analysis of the equation is facilitated since then it can be related to the schrodinger equation with quasiperiodic potential we show that the equation does indeed exhibit strange nonchaotic attractors and we consider the important question of whether these attractors are typical in the sense that they exist on a set of positive lebesgue measure in parameter space the equation also exhibits two and three frequency quasiperiodic behavior we also show that the strange nonchaotic attractors have distinctive frequency spectrum this property might make them experimentally observable

approximation by polynomials in two diffeomorphisms soit 1 k z et soient f et g des diffeomorphismes c k de c dans c ayant des degres opposes alors c f g est dense dans l espace de frechet c k c

large solutions to the monge ampere equations with nonlinear gradient terms existence and boundary behavior abstract in this paper we obtain conditions about the existence and boundary behavior of strictly convex solutions to the monge ampere equations with boundary blow up det d 2 u x b x f u x u q x u and det d 2 u x b x f u x 1 u q x u where is a strictly convex bounded smooth domain in r n with n 2 q 0 n or q 0 n b c which is positive in but may vanish or blow up on the boundary f c 0 f 0 0 and f is strictly increasing on 0 or f c r f s 0 s r and f is strictly increasing on r

strange attractors that are not chaotic abstract it is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic here we use the word strange to refer to the geometry or shape of the attracting set while the word chaotic refers to the dynamics of orbits on the attractor in particular the exponential divergence of nearby trajectories we first give examples for which it can be demonstrated that there is a strange nonchaotic attractor these examples apply to a class of maps which model nonlinear oscillators continuous time which are externally driven at two incommensurate frequencies it is then shown that such attractore are persistent under perturbations which preserve the original system type i e there are two incommensurate external driving frequencies this suggests that for systems of the typw which we have considered nonchaotic strange attractors may be expected to occur for a finite interval of parameter values on the other hand when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observed to be converted to a periodic or chaotic orbit thus we conjecture that in general continuous time systems flows which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space

some more universal scaling laws for critical mappings we study such nonlinear mappingsxn 1 f xn bcr of an intervali into itself for which the feigenbaum scaling laws hold i e for which bcr is an accumulation point of bifurcation points letx0 be a random variable with some absolutely continuous distribution ini we show in particular that i the geometric average distance ofxn from the nearest point of the attractor decreases liken 1 93387 ii the geometric average of xn x0 increases liken0 60 iii the geometric mean distance xn yn between the iterates of two close by pointsx0 y0 asymptotically tends towards a value x0 y0 0 77 these and other properties are also borne out from a simple probabilistic model which depicts the evolution as a random walklike process

critical phonons of the supercritical frenkel kontorova model renormalization bifurcation diagrams abstract the phonon modes of the frenkel kontorova model are studied both at the pinning transition as well as in the pinned cantorus phase we focus on the minimal frequency of the phonon spectrum and the corresponding generalized eigenfunction using an exact decimation scheme the eigenfunctions are shown to have non trivial scaling properties not only at the pinning transition point but also in the cantorus regime therefore the phonons defy localization and remain critical even where the associated area preserving map has a positive lyapunov exponent in this region the critical scaling properties vary continuously and are described by a line of renormalization limit cycles interesting renormalization bifurcation diagrams are obtained by monitoring the cycles as the parameters of the system are varied from an integrable case to the anti integrable limit both of these limits are described by a trivial decimation fixed point very surprisingly we find additional special parameter values in the cantorus regime where the renormalization limit cycle degenerates into the trivial fixed point at these degeneracy points the phonon hull is represented by an infinite series of step functions this novel behavior persists in the extended version of the model containing two harmonics additional richnesses of this extended model are the one to two hole transition line characterized by a divergence in the renormalization cycles non exponentially localized phonons and the preservation of critical behavior all the way upto the anti integrable limit

universal renormalization group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics we uncover the dynamics at the chaos threshold m of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period doubling cascade that occurs for m m we corroborate this structure analytically via the feigenbaum renormalization group rg transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential of which we determine the q index and the q generalized lyapunov coefficientl q our results are an unequivocal validation of the applicability of the nonextensive generalization of boltzmann gibbs statistical mechanics to critical points of nonlinear maps critical points of nonlinear maps offer a suitable playground for testing the validity of the nonextensive generalization of the boltzmann gibbs bg statistical mechanics proposed by tsallis over a decade ago 1 2 here we describe universal properties related to the dynamics of iterates at the onset of chaos in unimodal maps 3 which provide a literal confirmation of the generalized nonextensive theory to this end we employ the celebrated one dimensional logistic map f m x 512muxu 2 21 x 1 and the properties of its renormalization group rg fixed point to present evidence of previously unexposed scaling properties at the onset of chaos m5m at this state the most prominent of the map critical points the trajectories of the iterates exhibit an intricate structure that we describe and show is governed by the feigenbaum rg transformation 3 the domain of validity of bg statistical mechanics has been implicitly challenged by the proposal of its nonextensive generalization subsequent studies have offered experimental and numerical evidence that point out both the inadequacy of the standard bg statistics and the plausible competence of the generalized theory in describing various types of phenomena and systems this theoretical development represents an exceptional event in the long and trustworthy history of bg statistical mechanics however it is still in the process of being converted into a rigorously corroborated and fully understood fact the suggested circumstances under which the generalized theory is believed to be applicable at least with regards to nonlinear dynamical systems are those associated to a phase space with power law sensitivity to initial conditions to the consequent vanishing of the largest lyapunov exponent and to a fractal or multifractal geometrical structure 2 here we show that our results for the dynamics at the onset of chaos in unimodal maps constitute an unequivocal proof of the universal validity of the nonextensive statistics at such critical points in fact at the chaos threshold as well as at other critical points of the map the lyapunov exponent l 1 vanishes and the sensitivity to initial conditions j t for large iteration time t ceases to obey exponential behavior exhibiting instead a power law behavior 4 in order to describe the dynamics at such critical points the q exponential expression

fluctuating dynamics at the quasiperiodic onset of chaos tsallis q statistics and mori s q phase thermodynamics abstract we analyze the fluctuating dynamics at the golden mean transition to chaos in the critical circle map and find that trajectories within the critical attractor consist of infinite sets of power laws mixed together we elucidate this structure assisted by known renormalization group rg results next we proceed to weigh the new findings against tsallis entropic and mori s thermodynamic theoretical schemes and observe behavior to a large extent richer than previously reported we find that the sensitivity to initial conditions t has the form of families of intertwined q exponentials of which we determine the q indexes and the generalized lyapunov coefficient spectra q further the dynamics within the critical attractor is found to consist of not one but a collection of mori s q phase transitions with a hierarchical structure the value of mori s thermodynamic field variable q at each transition corresponds to the same special value for the entropic index q we discuss the relationship between the two formalisms and indicate the usefulness of the methods involved to determine the universal trajectory scaling function and or the occurrence and characterization of dynamical phase transitions

spectral analysis of deformed random networks we study spectral behavior of sparsely connected random networks under the random matrix framework subnetworks without any connection among them form a network having perfect community structure as connections among the subnetworks are introduced the spacing distribution shows a transition from the poisson statistics to the gaussian orthogonal ensemble statistics of random matrix theory the eigenvalue density distribution shows a transition to the wigner s semicircular behavior for a completely deformed network the range for which spectral rigidity measured by the dyson mehta ensuremath delta 3 statistics follows the gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure the spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure whereas the density distribution and the ensuremath delta 3 statistics remain identical to the undeformed network on the other hand the ensuremath delta 3 statistics is useful for the larger deformation strengths finally we analyze the spectrum of a protein protein interaction network for helicobacter and compare the spectral behavior with those of the model networks

bounded strictly pseudoconvex domains in c2 with obstruction flat boundary ii abstract on a bounded strictly pseudoconvex domain in c n n 1 the smoothness of the cheng yau solution to fefferman s complex monge ampere equation up to the boundary is obstructed by a local cr invariant of the boundary for a bounded strictly pseudoconvex domain c 2 diffeomorphic to the ball we prove that the global vanishing of this obstruction implies biholomorphic equivalence to the unit ball subject to the existence of a holomorphic vector field satisfying a mild approximate tangency condition along the boundary in particular by considering the euler vector field multiplied by i the result applies to all domains in a large c 1 open neighborhood of the unit ball in c 2 the proof rests on establishing an integral identity involving the cr curvature of for any holomorphic vector field defined in a neighborhood of the boundary the notion of ambient holomorphic vector field along the cr boundary generalizes naturally to the abstract setting and the corresponding integral identity still holds in the case of abstract cr 3 manifolds

fractalization of a torus as a strange nonchaotic attractor fractalization of a torus and its transition to chaos in a quasiperiodically forced logistic map is reinvestigated in relation to a strange nonchaotic attractor with the aid of a functional equation for the invariant curve the existence of a fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor as well as the fourier mode analysis mechanisms of the onset of a fractal torus and the transition to chaos are studied in connection with the intermittency

variation of total q prime curvature on cr manifolds abstract we derive variational formulas for the total q prime curvature under the deformation of strictly pseudoconvex domains in a complex manifold we also show that the total q prime curvature agrees with the renormalized volume of such domains with respect to the complete kahler einstein metric

weighted bergman kernels and quantization let be a bounded pseudoconvex domain in c n two positive functions on such that log log are plurisubharmonic and z a point at which log is smooth and strictly plurisubharmonic we show that as k the bergman kernels with respect to the weights k have an asymptotic expansion for x y near z where x y is an almost analytic extension of phi x x x and similarly for further if in addition is of finite type behave reasonably at the boundary and log log are strictly plurisubharmonic on we obtain also an analogous asymptotic expansion for the berezin transform and give applications to the berezin quantization finally for smoothly bounded and strictly pseudoconvex and a smooth strictly plurisubharmonic defining function for we also obtain results on the berezin toeplitz quantization

routes to chaos universality and glass formation abstract we review recent results obtained for the dynamics of incipient chaos these results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps namely the period doubling intermittency and quasiperiodicity routes in these situations the dynamical behavior is exactly describable through infinite families of tsallis q exponential functions furthermore the addition of a noise perturbation to the dynamics at the onset of chaos of the logistic map allows to establish parallels with the behavior of supercooled liquids close to glass formation specifically the occurrence of two step relaxation aging with its characteristic scaling property and subdiffusion and arrest is corroborated for such a system

convergence to the critical attractor of dissipative maps log periodic oscillations fractality and nonextensivity for a family of logisticlike maps we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space we found that the phase space volume occupied by the ensemble w t depicts a power law decay with log periodic oscillations reflecting the multifractal character of the critical attractor we explore the parametric dependence of the power law exponent and the amplitude of the log periodic oscillations with the attractor s fractal dimension governed by the inflection of the map near its extremal point further we investigate the temporal evolution of w t for the circle map whose critical attractor is dense in this case we found w t to exhibit a rich pattern with a slow logarithmic decay of the lower bounds these results are discussed in the context of nonextensive tsallis entropies

intermittency route to strange nonchaotic attractors in a non skew product map whether strange nonchaotic attractors snas can typically arise in non skew product maps has been a crucial question for more than two decades recently it was shown that snas arise in a particular non skew product map related to quasiperiodically driven continuous dynamical systems r badard chaos solitons fractals 28 1327 2006 chaos 18 023127 2008 in the present paper we derive badard s non skew product map from a periodically driven continuous dynamical system with spatially quasiperiodic potential and investigate onset mechanisms of snas in the map in particular we focus on a transition route to intermittent snas where snas appear after pair annihilations of stable and unstable fixed points located on a ring shaped invariant curve then the mean residence time and rotation numbers have a logarithmic singularity finally we discuss the existence of snas in a special class of non skew product maps

power law distribution of degree degree distance a better representation of the scale free property of complex networks whether real world complex networks are scale free or not has long been controversial recently in broido and clauset a d broido a clauset nat commun 10 1017 2019 it was claimed that the degree distributions of real world networks are rarely power law under statistical tests here we attempt to address this issue by defining a fundamental property possessed by each link the degree degree distance the distribution of which also shows signs of being power law by our empirical study surprisingly although full range statistical tests show that degree distributions are not often power law in real world networks we find that in more than half of the cases the degree degree distance distributions can still be described by power laws to explain these findings we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted two way selection process the model does not always produce solid power law distributions but predicts that the degree degree distance distribution exhibits stronger power law behavior than the degree distribution of a finite size network especially when the network is dense we test the strength of our model and its predictive power by examining how real world networks evolve into an overly dense stage and how the corresponding distributions change we propose that being scale free is a property of a complex network that should be determined by its underlying mechanism e g preferential attachment rather than by apparent distribution statistics of finite size we thus conclude that the degree degree distance distribution better represents the scale free property of a complex network

local polynomial convexity of graphs of functions in several variables abstract in this paper we investigate the locally polynomial convexity of graphs of smooth functions in several variables we also give a sufficient condition for a real analytic function g defined near 0 in c which behaves like z n near the origin so that the algebra generated by z m and g is dense in the space of continuous functions on d for all disks d close enough to the origin in c

golden mean renormalization for the harper equation the strong coupling fixed point we construct a renormalization fixed point corresponding to the strong coupling limit of the golden mean harper equation we give an analytic expression for this fixed point establish its existence and uniqueness and verify properties previously seen only in numerical calculations the spectrum of the linearization of the renormalization operator at this fixed point is also explicitly determined this strong coupling fixed point also helps describe the onset of a strange nonchaotic attractor in quasiperiodically forced systems

the local polynomial hull near a degenerate cr singularity bishop discs revisited let be a smooth real surface in and let be a point at which the tangent plane is a complex line how does one determine whether or not is locally polynomially convex at such a p i e at a cr singularity even when the order of contact of with at p equals 2 no clean characterisation exists difficulties are posed by parabolic points hence we study non parabolic cr singularities we show that the presence or absence of bishop discs around certain non parabolic cr singularities is completely determined by a maslov type index this result subsumes all known facts about bishop discs around order two non parabolic cr singularities sufficient conditions for bishop discs have earlier been investigated at cr singularities having high order of contact with these results relied upon a subharmonicity condition which fails in many simple cases hence we look beyond potential theory and refine certain ideas going back to bishop

influence of global correlations on central limit theorems and entropic extensivity abstract we consider probabilistic models of n identical distinguishable binary random variables if these variables are strictly or asymptotically independent then for n i the attractor in distribution space is according to the standard central limit theorem a gaussian and ii the boltzmann gibbs shannon entropy s bgs i 1 w p i ln p i where w 2 n is extensive meaning that s bgs n n if these variables have any nonvanishing global i e not asymptotically independent correlations then the attractor deviates from the gaussian the entropy appears to be more robust in the sense that in some cases s bgs remains extensive even in the presence of strong global correlations in other cases however even weak global correlations make the entropy deviate from the normal behavior more precisely in such cases the entropic form s q 1 q 1 1 i 1 w p i q with s 1 s bgs can become extensive for some value of q 1 this scenario is illustrated with several new as well as previously described models the discussion illuminates recent progress into q describable nonextensive probabilistic systems and the conjectured q central limit theorem q clt which posses a q gaussian attractor