measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

random perturbations of heteroclinic attractors estimates are derived for the mean recurrence time of orbits in the neighborhood of an attracting homoclinic orbit or heteroclinic cycle in an ordinary differential equation subject to small additive random noise the theory presented is illustrated with numerical simulations of several systems including ones invariant under symmetry groups for which such heteroclinic attractors are structurally stable the physical implications of the work presented are briefly discussed

the inverse eigenvalue problem for nonnegative matrices abstract let a be a nonnegative matrix with spectrum 1 2 m and b be a nonnegative matrix with spectrum 1 2 n where 1 is the perron eigenvalue of b furthermore let a maximal diagonal element of a be greater than or equal to 1 in the article we construct a nonnegative matrix c with spectrum 1 2 m 2 n this construction enables us to obtain several results on how to determine new realizable lists from known realizable lists

on the eckhaus instability for spatially periodic patterns abstract the range of stable wavevectors is near the threshold for appearance of periodic patterns in quasi one dimensional systems limited by the long wavelength eckhaus instability at this instability saddle point solutions characterizing the wavelength changing processes inside the stable range merge with the periodic solutions we first analyse this bifurcation near threshold using the amplitude expansion in lowest order then a nonlinear equation for the evolution of slow modulations of the periodic pattern far from threshold but near the eckhaus instability is derived and used to analyse the universal properties of the eckhaus bifurcation more detailed information concerning the spatial symmetry of saddle point solutions is obtained by numerical integration of simple model systems

analysis of excitability for the fitzhugh nagumo model via a stochastic sensitivity function technique we study excitability phenomena for the stochastically forced fitzhugh nagumo system modeling a neural activity noise induced changes in the dynamics of this model can be explained by the high stochastic sensitivity of its attractors computational methods based on the stochastic sensitivity functions technique are suggested for the analysis of these attractors our method allows us to construct confidence ellipses and estimate a threshold value of a noise intensity corresponding to the neuron excitement on the basis of the proposed technique a supersensitive limit cycle is found for the fitzhugh nagumo model

improved moser trudinger type inequalities in the hyperbolic space hn we establish an improved version of the moser trudinger inequality in the hyperbolic space hnhn n 2n 2 namely we prove the following result for any 0 n 1nn then we have supu c0 hn hn gu gndvolg hn u ndvolg 1 hn n n u nn 1 dvolg where n n n 11n 1 n 1 n 1 denotes the surface area of the unit sphere in rnrn and n t et j 0n 2tjj this improves the moser trudinger inequality in hyperbolic spaces obtained recently by mancini and sandeep 2010 by mancini et al 2013 and by adimurthi and tintarev 2010 for 0 0 in the limiting case n 1n n we prove a moser trudinger inequality with exact growth in hnhn supu c0 hn hn gu gndvolg n 1n n hn u ndvolg 11 hn u ndvolg hn n n u nn 1 1 u nn 1dvolg this improves the moser trudinger inequality with exact growth in hnhn established by lu and tang 2016 these inequalities are achieved from the comparison of the symmetric non increasing rearrangement of a function both in the hyperbolic and the euclidean spaces and the same inequalities in the euclidean space this approach seems to be new comparing with the previous ones

symmetry and bifurcations of momentum mappings the zero set of a momentum mapping is shown to have a singularity at each point with symmetry the zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function the proof uses the kuranishi theory of deformations among the applications it is shown that the set of all solutions of the yang mills equations on a lorentz manifold has a singularity at any solution with symmetry in the sense of a pure gauge symmetry similarly the set of solutions of einstein s equations has a singularity at any solution that has spacelike killing fields provided the spacetime has a compact cauchy surface

the symmetric nonnegative inverse eigenvalue problem for 5 5 matrices abstract the symmetric nonnegative inverse eigenvalue problem sniep asks when a list 1 2 n of n real numbers is the spectrum of an n n symmetric nonnegative matrix this problem is completely solved only for n 4 our main goal here is to contribute to the solution of sniep for n 5 we also give a sufficient condition for a list to be realized as the spectrum of a symmetric positive matrix

nonequilibrium phenomena outlines and bibliographies of a workshop the following is a set of outlines and bibliographies for lectures presented at a summer workshop on nonequilibrium phenomena held from june 22 to july 3 1981 at the institute for theoretical physics in santa barbara these outlines were distributed to the participants in lieu of formal proceedings and they are being presented for publication in the same form in the belief that the information they contain will be useful to a wider audience it should be clearly stated however that the compilation is an informal one which does not claim to be a complete survey of the subject

fourier analysis and optimal hardy adams inequalities on hyperbolic spaces of any even dimension abstract recently the second and third authors established the sharp hardy adams inequalities of second order derivatives with the best constants on the hyperbolic space b 4 of dimension four 40 adv math 2017 a key method used in dimension four in 40 is that the following hardy operator when n 4 and k 2 b n k u 2 d x i 1 k 2 i 1 2 b n u 2 1 x 2 2 k d x can be decomposed exactly as the product of fractional laplacians however such a decomposition in dimension four is no longer possible in the case n 4 and 2 k n 2 and the situation here is thus considerably more difficult and complicated therefore it remains open as whether a sharp hardy adams inequality still holds on higher dimensional hyperbolic space b n for n 4 the main purpose of this paper is to use a substantially new method of estimating the hardy operator to establish the sharp hardy adams inequalities on hyperbolic spaces b n for all even dimension n and n 4 as applications of such inequalities we will improve substantially the known adams inequalities on hyperbolic space b n in the literature and also strengthen the classical adams inequality and the hardy inequality on euclidean balls in any even dimension the later inequality can be viewed as the borderline case of the sharp hardy sobolev maz ya inequalities for higher order derivatives in high dimensions obtained recently by the second and third authors 41

the nonnegative inverse eigenvalue problem from the coefficients of the characteristic polynomial ebl digraphs the nonnegative inverse eigenvalue problem niep is given a family of complex numbers 1 n find necessary and sufficient conditions for the existence of a nonnegative matrix a of order n with spectrum loewy and london r loewy d london a note on the inverse eigenvalue problems for nonnegative matrices linear and multilinear algebra 6 1978 83 90 resolved it for n 3 and for n 4 when the spectrum is real in our way of handling the niep we focus our attention on the coefficients of the characteristic polynomial of a thus the niep that we consider is given k1 k2 kn real numbers find necessary and sufficient conditions for the existence of a nonnegative matrix a of order n with characteristic polynomial xn k1xn 1 k2xn 2 kn the coefficients of the characteristic polynomial are closely related to the cyclic structure of the weighted digraph with adjacency matrix a we introduce a special type of digraph structure that we shall call ebl in which this relation is specially simple we give some results that show the interest of ebl structures we completely solve the niep from the coefficients of the characteristic polynomial for n 4 we also solve a special case of the niep for n 2p 1 with k1 kp 1 0 and p 2

estimating correlation dimension from a chaotic time series when does plateau onset occur abstract suppose that a dynamical system has a chaotic attractor a with a correlation dimension d 2 a common technique to probe the system is by measuring a single scalar function of the system state and reconstructing the dynamics in an m dimensional space using the delay coordinate technique the estimated correlation dimension of the reconstructed attractor typically increases with m and reaches a plateau on which the dimension estimate is relatively constant for a range of large enough m values the plateaued dimension value is then assumed to be an estimate of d 2 for the attractor in the original full phase space in this paper we first present rigorous results which state that for a long enough data string with low enough noise the plateau onset occurs at m ceil d 2 where ceil d 2 standing for ceiling of d 2 is the smallest integer greater than or equal to d 2 we then numerical examples illustrating the theoretical prediction in addition we discuss new findings showing how practical factors such as a lack of data and observational noise can produce results that may seem to be inconsistent with the theoretically predicted plateau onset at m ceil d 2

sharp moser trudinger inequality on the heisenberg group at the critical case and applications let h cn r be the n dimensional heisenberg group q 2n 2 be the homogeneous dimension of h q qq 1 and z 4 t2 14 be the homogeneous norm of z t h then we prove the following sharp moser trudinger inequality on h theorem 1 6 there exists a positive constant q q 2 n 12 q 12 q2 1 n 1 q 1 such that for any pair satisfying 0 q 0 q 1 q there holds sup u 1 1 h1 exp u q q 1 k 0q 2 kk u kq q 1 c q the constant q 1 q is best possible in the sense that the supremum is infinite if q 1 q here is any positive number and u 1 h hu q h u q 1 q our result extends the sharp moser trudinger inequality by cohn and lu 2001 19 on domains of finite measure on h and sharpens the recent result of cohn et al 2012 18 where such an inequality was studied for the subcritical case q 1 q we carry out a completely different and much simpler argument than that in cohn et al 2012 18 to conclude the critical case our method avoids using the rearrangement argument which is not available in an optimal way on the heisenberg group and can be used in more general settings such as riemanian manifolds appropriate metric spaces etc as applications we establish the existence and multiplicity of nontrivial nonnegative solutions to certain nonuniformly subelliptic equations of q laplacian type on the heisenberg group theorems 1 8 1 9 1 10 and 1 11 divh hu q 2 hu v u q 2u f u eh with nonlinear terms f of maximal exponential growth exp u qq 1 as u in particular when e 0 the existence of a nontrivial solution is also given

exponential decay of power spectra at high frequency and positive lyapunov exponents abstract it is generally accepted that power spectra of time series taken from continuous time dynamical systems exhibiting deterministic chaos will decay exponentially at high frequency the exponential decay constant is an inverse time scale that is an invariant of the dynamics of the system and that is unique to deterministic chaos theoretical arguments are presented that suggest that should be related to the positive lyapunov exponents numerical results are presented from four models with attractor dimensions ranging from 2 009 to 20 28 which suggest that is roughly proportional to the sum of the positive lyapunov exponents i for these models the ratio of to i lies between the values 0 639 and 2 46 and shows no systematic change with attractor dimension

elgenvalues of nonnegative matrices abstract in a partial continuation of work by fiedler some spectral properties of symmetric nonnegative matrices are extended to general nonnegative matrices

nonlinear dynamical analysis of speech this paper reports results of the estimation of dynamical invariants namely lyapunov exponents dimension and metric entropy for speech signals two optimality criteria from dynamical systems literature namely singular value decomposition method and the redundancy method are used to reconstruct state space trajectories of speech and make observations the positive values of the largest lyapunov exponent of speech signals in the form of phoneme articulations show the average exponential divergence of nearby trajectories in the reconstructed state space the dimension of a time series is a measure of its complexity and gives bounds on the number of state space variables needed to model it it is found that most speech signals in the form of phoneme articulations are low dimensional for comparison a statistical model of a speech time series is also used to estimate the correlation dimension the second order dynamical entropy which is a lower bound of metric entropy of speech time series is found to

block matrices and guo s index for block circulant matrices with circulant blocks abstract in this paper we deal with circulant and partitioned into n by n circulant blocks matrices and introduce spectral results concerning this class of matrices the problem of finding lists of complex numbers corresponding to a set of eigenvalues of a nonnegative block matrix with circulant blocks is treated along the paper we call realizable list if its elements are the eigenvalues of a nonnegative matrix the guo s index 0 of a realizable list is the minimum spectral radius such that the list up to the initial spectral radius together with 0 is realizable the guo s index of block circulant matrices with circulant blocks is obtained and in consequence necessary and sufficient conditions concerning the niep nonnegative inverse eigenvalue problem for the realizability of some spectra are given

a new approach to sharp moser trudinger and adams type inequalities a rearrangement free argument abstract the main purpose of this paper is two fold on the one hand we will develop a new approach to establish sharp singular moser trudinger and adams type inequalities in unbounded domains of euclidean spaces without using the standard symmetrization on the other hand we will prove the sharp singular adams type inequality on high order sobolev spaces w m n m r n of arbitrary integer order m theorem 1 1 which improves the results of ruf and sani 2013 48 where sharp adams inequalities were established for even m and those of the authors lam and lu 2012 28 29 for odd m but with different and more restricted norms we first establish the sharp local singular adams inequality on domains in r n of finite measure theorem 1 4 we take a perspective that any function in the high order sobolev spaces w m n m r n can be represented as a bessel potential thus we can fully use the tools from harmonic analysis and the kernel properties of the polyharmonic operators i m 2 once we have established this sharp local adams inequality then we can adapt the rearrangement free method we will develop in this paper to derive a global sharp adams inequality from a local one our argument substantially simplifies those in ruf and sani 2013 48 and lam and lu 2012 28 29 and avoids the use of rather deep and complicated comparison principle of solutions to polyharmonic operators used in ruf and sani 2013 48 lam and lu 2012 28 29 moreover our theorem holds on sobolev spaces w n r n of any positive fractional order n theorems 1 6 and 1 7 as consequences we can also establish sharp adams inequalities with less restrictions on the sobolev norms see theorems 1 2 1 3 and 1 5 our approach is surprisingly simple and general and can be easily applied to scenarios such as riemannian and sub riemannian manifolds where symmetrization argument does not work see e g on the heisenberg group lam and lu 2012 30

measurement of the lyapunov spectrum from a chaotic time series the exponential divergence or convergence of nearby trajectories lyapunov exponents is conceptually the most basic indicator of deterministic chaos we propose a new method to determine the spectrum of several lyapunov exponents including positive zero and even negative ones from the observed time series of a single variable we have applied the method to various known model systems and also to the rayleigh b enard experiment and have elucidated the dependence of the lyapunov exponents on the rayleigh number

quantifying the influence of initial values on non linear prediction motivated by the m step ahead prediction problem in non linear time series a brief sketch of stochastic chaotic systems is provided the accuracy of the prediction depends on the initial value which is a typical feature of non linear but not necessarily chaotic models however if the model is chaotic small noise can be amplified very quickly through time evolution at some initial values thereby decreasing dramatically the reliability of the prediction further if the model is chaotic small shifts in some initial values can lead to considerable errors in prediction which can be monitored by the newly defined lyapunov like indices for the nonparametric predictor constructed by the locally linear regression method the mean squared error may be decomposed into two parts the conditional variance and the divergence resulting from a small shift in initial values the decomposition also holds for more general predictors a consistent estimator of the lyapunov like index is also constructed by the locally linear regression method both simulated and real data are used as illustrations

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

a nonlinear dynamical systems analysis of fricative consonants acoustic waveforms of the strident fricatives s z sh and yog spoken by two native american english speakers are analyzed using modern chaotic analysis techniques fricative data are extracted from both intervocalic and sustained utterances for comparison acoustic waveforms of the vowels a i and u are also analyzed for 44 of the unvoiced fricative tokens in vcv contexts and 59 of the sustained voiced fricatives indications of low dimensional dynamics could be found with the given limitations of stationarity the low dimensional chaotic behavior is exhibited by a correlation dimension d2 ranging between 3 and 7 2 and by positive maximum lyapunov exponents les for the remaining fricatives results suggest that the dimensional complexity therein is greater than the maximum d2 value that could be reliably estimated from the available data about 7 8 for the intervocalic cases and 9 for the sustained cases intervocalic voiced fricatives are excluded from the analysis due to stat

the effect of distant side walls on the evolution and stability of finite amplitude rayleigh benard convection a recent study by cross et al 1980 has described a class of finite amplitude phase winding solutions of the problem of two dimensional rayleigh benard convection in a shallow fluid layer of aspect ratio 2 l 1 confined laterally by rigid side walls these solutions arise at rayleigh numbers r r 0 o l 1 where r 0 is the critical rayleigh number for the corresponding infinite layer nonlinear solutions of constant phase exist for rayleigh numbers r r 0 o l 2 but of these only the two that bifurcate at the lowest value of r are stable to two dimensional linearized disturbances in this range daniels 1978 in the present paper one set of the class of phase winding solutions is found to be stable to two dimensional disturbances for certain values of the prandtl number of the fluid and for stress free horizontal boundaries the results predict that to preserve stability there must be a continual readjustment of the roll pattern as the rayleigh number is raised with a corresponding increase in wavelength proportional to r r 0 these solutions also exhibit hysteresis as the rayleigh number is raised and lowered for other values of the prandtl number the number of rolls remains unchanged as the rayleigh number is raised and the wavelength remains close to its critical value it is proposed that the complete evolution of the flow pattern from a static state must take place on a number of different time scales of which t o r r 0 1 and t o r r 0 2 are the most significant when t o r r 0 1 the amplitude of convection rises from zero to its steady state value but the final lateral positioning of the rolls is only completed on the much longer time scale t o r r 0 2

effects of boundaries on one dimensional reaction diffusion equations near threshold a simple set of two reaction diffusion equations is analyzed near the threshold for the appearance of spatially periodic solutions in one dimension exact amplitude equations are derived to second order in the deviation from the threshold wavevector selection is studied analytically for parameters varying slowly in space from supercritical to subcritical conditions the nonuniversality of the selection process is demonstrated explicitly for nonpotential cases the effect of boundary conditions on restricting the available band of wavevectors is studied for solutions which fall below their bulk value near the boundary type i the existence of another class of static solutions type ii remaining finite at the boundary even near threshold is demonstrated a linear stability analysis of the uniform state reveals that type i solutions are often unstable immediately above threshold then one has type ii states or oscillatory solutions some numerical results are presented which confirm the analytic calculations

noisy precursors of nonlinear instabilities this paper studies the effect of external noise on systems displaying nonlinear instabilities of periodic orbits each class of instability is found to have its own characteristic signature as displayed by the power spectrum results are derived for each of the codimension one instabilities familiar from bifurcation theory

realizable lists on a class of nonnegative matrices abstract a square matrix of order n with n 2 is called permutative matrix when all its rows are permutations of the first row in this paper recalling spectral results for partitioned into 2 by 2 symmetric blocks matrices sufficient conditions on a given complex list to be the list of the eigenvalues of a nonnegative permutative matrix are given in particular we study niep and pniep when some complex elements in the lists under consideration have non zero imaginary part realizability regions for nonnegative permutative matrices are obtained a guo s realizability preserving perturbations result is obtained

realizable lists via the spectra of block matrices abstract in this paper we present spectral results for matrices partitioned into higher order blocks where not all blocks are necessarily square using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative matrix are obtained and the corresponding matrix is constructed in particular spectral results for symmetric matrices are derived a result on guo perturbations for permutative matrices on given lists is generalized

realizable lists via the spectra of structured matrices abstract a square matrix of order n with n 2 is called a permutative matrix or permutative when all its rows up to the first one are permutations of precisely its first row in this paper the spectra of a class of permutative matrices are studied in particular spectral results for matrices partitioned into 2 by 2 symmetric blocks are presented and using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative permutative matrix are obtained and the corresponding permutative matrices are constructed guo perturbations on given lists are exhibited

chaotic attractors of an infinite dimensional dynamical system abstract we study the chaotic attractors of a delay differential equation the dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of lyapunov exponents according to a conjecture of kaplan and yorke assuming this conjecture to be valid as the delay parameter is varied from computations of the spectrum of lyapunov exponents we observe a roughly linear increase from two to twenty in the dimension while the metric entropy remains roughly constant these results are compared to a linear analysis and the asymptotic behavior of the lyapunov exponents is derived

on the nonnegative eigenvalue problem abstract 1 1 n is the spectrum of a stochastic matrix of order n 1 if and only if there exists some real matrix b of order n with spectrum 1 n and some n simplex s r n containing the origin such that bs s this result appears implicitly in ciarlet s work and it provides us with a geometrical tool to obtain sufficient conditions for the nonnegative eigenvalue problem we employ it here to generalize the sufficient conditions given by kellogg

extracting qualitative dynamics from experimental data abstract we consider the notion of qualitative information and the practicalities of extracting it from experimental data our approach based on a theorem of takens draws on ideas from the generalized theory of information known as singular system analysis due to bertero pike and co workers we illustrate our technique with numerical data from the chaotic regime of the lorenz model

ito versus stratonovich a survey is given of the facts and fancies concerning the nonlinear langevin or ito equation actually it is merely a pre equation which becomes an equation when an interpretation rule is added the rules of ito and stratonovich differ but both are mathematically consistent and therefore equally admissible conventions the reason why they seem to lead to physical differences is that the langevin approach used to arrive at the equation involves a tacit assumption for systems with external noise this assumption can be justified and it is then clear that the stratonovich rule applies systems with internal noise however can only be properly described by a master equation and the ito stratonovich controversy never enters afterward one is free to model the resulting fluctuations either with an ito or a stratonovich scheme but that does not lead to any new information

amplification and damping of deterministic noise in coupled cellular arrays abstract large scale spatiotemporal organization and enhanced periodicity are seen when a population of chaotic rossler attractors is coupled through one or more of the variables the resulting periodicity has been analyzed by means of return maps and by the projection of these maps as state variable dispersion histograms self mapping of cells in the array within dispersion criteria yielded evidence of reverse bifurcation sequences f 8 4 2 1 expressed in the behavior of most of the 900 to 25 600 individual cells self mapping is seen in spiral and periodic banded fields but not in turbulent fields or in synchronous chaos coupling of arrays of periodic attractors leads to dispersion in self mapping similar to that seen in the coupled chaotic arrays fixed patterns representing the bifurcation sequences that occur in these arrays were overlaid on the spiral field portraits

on lie groups and hyperbolic symmetry from kunze stein phenomena to riesz potentials abstract sharp forms of kunze stein phenomena on s l 2 r are obtained by using symmetrization and stein weiss potentials a new structural proof with remarkable simplicity can be given on s l 2 r which effectively transfers the analysis from the group to the symmetric space corresponding to a manifold with negative curvature our methods extend to include the lorentz groups and n dimensional hyperbolic space through application of the riesz sobolev rearrangement inequality a new framework is developed for riesz potentials on semisimple symmetric spaces and the semi direct product of groups analogous to the iwasawa decomposition for semisimple lie groups extensions to higher rank lie groups and analysis on multidimensional connected hyperboloids including anti de sitter space are suggested by the analysis outlined here

pattern competition and the decay of unstable patterns in quasi one dimensional systems abstract the dynamics of quasi one dimensional pattern forming systems with simple periodic initial conditions and additional noise or with almost periodic initial conditions is studied analytically and numerically using the lowest order amplitude equation in this way the decay of eckhaus unstable patterns and subsequent formation of stable ones as observed recently and the competition of patterns with different wavenumbers is studied

a partial differential equation with infinitely many periodic orbits chaotic oscillations of a forced beam this paper delineates a class of time periodically perturved evolution equations in a banach space whose associated poincar e map contains a smale horseshoe this implies that such systems possess periodic orbits with arbitrarily high period the method uses techniques originally due to melnikov and applies to systems of the form x f0 x f1 x t where x f0 x is hamiltonian and has a homoclinic orbit we give an example from structural mechanics sinusoidally forced vibrations of a buckled beam

guo s index for some classes of matrices abstract a permutative matrix is a square matrix such that every row is a permutation of the first row a circulant matrix is a matrix where each row is a cyclic shift of the row above to the right the guo s index 0 of a realizable list is the minimum spectral radius such that the list up to the initial spectral radius together with 0 is realizable the guo s index of some permutative matrices is obtained our results are constructive some examples designed using matlab are given at the end of the paper

chaos in segments from korean traditional singing and western singing the time series of the segments from a korean traditional song gwansanyungma and a western song la mamma morta were investigated using chaotic analysis techniques it is found that the phase portrait in the reconstructed state space of the time series of the segment from the korean traditional song has a more complex structure in comparison with the segment from the western songs the segment from the korean traditional song has the correlation dimension 4 4 and two positive lyapunov exponents which show that the dynamic related to the korean traditional song is a high dimensional hyperchaotic process on the other hand the segment from the western song with only one positive lyapunov exponent and the correlation dimension 2 5 exhibits low dimensional chaotic behavior

a simple stochastic model for the onset of turbulence in rayleigh benard convection abstract a simple stochastic model of a particle diffusing randomly in an external two well potential is proposed to stimulate the onset of turbulence in a medium aspect ratio cylindrical rayleigh benard cell the model is studied numerically and both time series and their power spectra are obtained the results are compared with experimental data as well as with the results of deterministic models consisting of a finite number of interacting modes

concept of complexity in random dynamical systems we introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system in dynamical systems with small random perturbations this indicator coincides with the rate k of divergence of nearby trajectories evolving under two different noise realizations the meaning of k is discussed in the context of the information theory and it is shown that it can be determined from real experimental data in the presence of strong dynamical intermittency the value of k is very different from the standard lyapunov exponent ensuremath lambda mathrm ensuremath sigma computed considering two nearby trajectories evolving under the same realization of the randomness however the former is much more relevant than the latter from a physical point of view as illustrated by some numerical computations for noisy maps and sandpile models textcopyright 1996 the american physical society

computation of lyapunov spectra effect of interactive noise and application to a chemical oscillator abstract a refined version of the sano sawada algorithm to compute lyapunov spectra has been implemented and tested with several models which include periodic chaotic and hyperchaotic attractors under conditions designed to mimic experimental situations it was found that reliable lyapunov exponents can be obtained for time series of moderate length and point density also in the presence of interactive noise as long as its amplitude does not exceed 1 of the oscillation amplitude the algorithm was then applied to experimental data from the co oxidation on pt 110 clearly showing the occurrence of chaos as well as hyperchaos

deterministic noise amplifiers although we are accustomed to considering only overall stability properties of dynamical systems local stability properties can also have a dramatic physical effect local instabilities in overall stable motion can cause otherwise imperceptible ambient noise to be amplified to macroscopic proportions the result can be easily mistaken for deterministic chaos we give measures for local instability and noise amplification in terms of the covariance matrix and local divergence rates and analyze several examples an experimental test can be made by varying the external noise level for sufficiently small amplitudes the noisy response due to local instabilities scales linearly with the noise level whereas noisy behavior due to deterministic chaos is largely unaffected

a hardy moser trudinger inequality abstract in this paper we obtain an inequality on the unit disk b in r 2 which improves the classical moser trudinger inequality and the classical hardy inequality at the same time namely there exists a constant c 0 0 such that b e 4 u 2 h u d x c 0 u c 0 b 0 where h u b u 2 d x b u 2 1 x 2 2 d x this inequality is a two dimensional analog of the hardy sobolev maz ya inequality in higher dimensions which has been intensively studied recently we also prove that the supremum is achieved in a suitable function space which is an analog of the celebrated result of carleson chang for the moser trudinger inequality

extreme nonnegative matrices abstract an entrywise nonnegative n n matrix a is extreme if its spectrum 1 n has the property that for all 0 1 n is not the spectrum of a nonnegative matrix it is proved that if a is an extreme nonnegative matrix then there exists a nonzero nonnegative matrix y such that ay ya and at y 0 where is the hadamard or entrywise product and t denotes transpose

construction of nonnegative symmetric matrices with given spectrum abstract let 1 n be the spectrum of a nonnegative symmetric matrix a with the perron eigenvalue 1 a diagonal entry c and let 1 m be the spectrum of a nonnegative symmetric matrix b with the perron eigenvalue 1 we show how to construct a nonnegative symmetric matrix c with the spectrum 1 max 0 1 c 2 n 2 m

applications of a brauer theorem in the nonnegative inverse eigenvalue problem abstract a result by brauer which shows how to modify one single eigenvalue of a matrix without changing any of the remaining eigenvalues plays a relevant role in the study of the nonnegative inverse eigenvalue problem niep perfect in a long time ignored paper 1955 presents an extension of this result which shows how to modify r eigenvalues of a matrix of order n r n via a rank r perturbation without changing any of the n r remaining eigenvalues by using this extension perfect gives a realizability criterion for the real niep which is not contained in soto s realizability criterion in this work by extending perfect s result we give a new realizability criterion for the real niep which contains soto s criterion thus this new realizability criterion appears to be the most general sufficient condition for the real niep so far we also contribute to the solution of the symmetric niep for n 5

sharp hardy adams inequalities for bi laplacian on hyperbolic space of dimension four abstract we establish sharp hardy adams inequalities on hyperbolic space b 4 of dimension four namely we will show that for any 0 there exists a constant c 0 such that b 4 e 32 2 u 2 1 32 2 u 2 d v 16 b 4 e 32 2 u 2 1 32 2 u 2 1 x 2 4 d x c for any u c 0 b 4 with b 4 h 9 4 h u u d v 1 as applications we obtain a sharpened adams inequality on hyperbolic space b 4 and an inequality which improves the classical adams inequality and the hardy inequality simultaneously the later inequality is in the spirit of the hardy trudinger moser inequality on a disk in dimension two given by wang and ye in 46 and on any convex planar domain by lu and yang in 33 the fourier analysis techniques on hyperbolic and symmetric spaces play an important role in our work

wavenumber selection and eckhaus instability in couette taylor flow abstract we review a number of experimental results which pertain to pattern selection in couette taylor flow they include measurements of the harmonic contents of taylor vortices of the location of the eckhaus boundary of wavenumber selection by a spatial ramp of the reynolds number and of the axial variation of the wavenumber in the finite system we show that many of the results can be understood quantitatively in terms of the ginzburg landau amplitude equation

guo perturbation for symmetric nonnegative circulant matrices abstract guo w guo eigenvalues of nonnegative matrices linear algebra appl 266 1997 261 270 sets the question if the list 1 2 n is symmetrically realizable that is is the spectrum of a symmetric nonnegative matrix and t 0 whether or not the list t 1 t 2 t 3 n is also symmetrically realizable in this paper we give an affirmative answer to this question in the case that the realizing matrix is circulant or left circulant we also give a necessary and sufficient condition for to be the spectrum of a nonnegative left circulant matrix

on the spectra of some g circulant matrices and applications to nonnegative inverse eigenvalue problem abstract a g circulant matrix a is defined as a matrix of order n where the elements of each row of a are identical to those of the previous row but are moved g positions to the right and wrapped around using number theory certain spectra of g circulant real matrices are given explicitly the obtained results are applied to nonnegative inverse eigenvalue problem to construct nonnegative g circulant matrices with given appropriated spectrum additionally some g circulant matrices are reconstructed from its main diagonal entries

melnikov s method and arnold diffusion for perturbations of integrable hamiltonian systems we start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates we use kolmogorov arnold moser kam theory to show that some of the resulting tori persist under small perturbations and use a vector of melnikov integrals to show that under suitable hypotheses their stable and unstable manifolds intersect transversely this transverse intersection is ultimately responsible for arnold diffusion on each energy surface the method is applied to a pendulum oscillator system

nonlinear dynamic analysis of voices before and after surgical excision of vocal polyps phase space reconstruction correlation dimension and second order entropy methods from nonlinear dynamics are used to analyze sustained vowels generated by patients before and after surgical excision of vocal polyps two conventional acoustic perturbation parameters jitter and shimmer are also employed to analyze voices before and after surgery presurgical and postsurgical analyses of jitter shimmer correlation dimension and second order entropy are statistically compared correlation dimension and second order entropy show a statistically significant decrease after surgery indicating reduced complexity and higher predictability of postsurgical voice dynamics there is not a significant postsurgical difference in shimmer although jitter shows a significant postsurgical decrease the results suggest that jitter and shimmer should be applied to analyze disordered voices with caution however nonlinear dynamic methods may be useful for analyzing abnormal vocal function and quantitatively evaluating the effects of surgical excision of vocal polyps