subharmonic and homoclinic bifurcations in a parametrically forced pendulum abstract depending on the parameters of a parametrically forced pendulum system the boundaries of subharmonic and homoclinic bifurcations are calculated on the basis of the melnikov method and of averaging methods it is shown that as a parameter is varied repeated resonances of successively higher periods occur culminating in homoclinic orbits according to the theorem of smale homoclinic bifurcation is the source of the unstable chaotic motions observed for some selected parameter sets the theoretical predictions are tested by numerical calculations very good agreement is found between analytical and numerical results

influence of observational noise on the recurrence quantification analysis in this paper we estimate the errors due to observational noise on the recurrence quantification analysis rqa based on this estimation we present ways to minimize these errors we give a criterion to choose the threshold e needed for the optimal computation of the recurrence plot rp one important point is to show the limits of interpretability of the results of the rqa if it is applied to measured time series we show that even though the rqa is very susceptible to observational noise it can yield reliable results for an optimal choice of e if the noise level is not too high we apply the results to typical models such as white noise the logistic map and the lorenz system and to experimental laser data

associativity of quantum multiplication we proved the associativity of the multiplication of quantum cohomology for a monotone compact symplectic manifold v for which c 1 a 1 for any effective class the same proof also works for any positive compact symplectic manifold with c 1 a 1

from taubes currents to almost kahler forms the taubes current is introduced by taubes in j symplectic geom 9 161 250 2011 as an intermediate step to construct almost kahler forms in this paper we prove that an almost complex structures being almost kahler structure in dimension four is the equivalent of the existence of taubes currents precisely we show that taubes currents could be regularized to almost kahler forms up to small perturbations of cohomology classes on any 4 dimensional almost complex manifold m j a similar result is established for higher dimensions under the assumption of almost kahler an application to donaldson s tamed to compatible question is provided

emd based refined composite multiscale entropy analysis of complex signals abstract multiscale entropy mse is an effective method to measure the complexity of signals from complex systems which has been applied to various fields successfully however mse may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse graining procedure reduces the length of data considerably at large scales refined composite multiscale entropy rcmse is then developed to solve this problem however trends superimposed in signals may significantly affect the complexity measurement thus we introduce an empirical mode decomposition based rcmse called emd rcmse to first eliminate such effects of trends and then measure the complexity of signals it is validated from simulated signals and has good estimation in addition this method is also applied to study the complexity of traffic signals and we obtain some interesting results 1 traffic signals are more complex than the results showing from rcmse mse 2 weekday and weekend patterns different combination of trends greatly affect the results 3 complexity indices change with time at each day due to the degree of human activities

stationary discs and finite jet determination for non degenerate generic real submanifolds abstract let m c n be a generic real submanifold of class c 4 in case m is levi non degenerate in the sense tumanov we construct stationary discs for m if furthermore m satisfies an additional non degeneracy condition we apply the method of stationary discs to obtain 2 jet determination of cr automorphisms of m

integrity measures quantifying the erosion of smooth and fractal basins of attraction abstract the phase portraits of a dissipative dynamical system are characterized by the existence of one or more stable attractors which typically include point equilibria periodic oscillations harmonic and subharmonic quasi periodic solutions and chaotic attractors each attractor is embedded in its own domain or basin of attraction bounded by a separatrix associated with an unstable saddle solution under the variation of a control parameter as the attractors move and bifurcate the basins also undergo corresponding changes and metamorphoses these changes in size and shape are usually continuous but can be discontinuous as when an attractor vanishes along with its basin at a saddle node bifurcation associated with the homoclinic tangling of the invariant manifolds of the saddle solution basin boundaries can also change in nature from smooth to fractal in this paper the escape of a driven oscillator from a cubic potential well as an archetypal example is used to explore the engineering significance of the basin erosions that occur under increased forcing various measures of engineering integrity of the constrained attractor are introduced a global measure assesses the overall basin area a local measure assesses the distance from the attractor to the basin boundary and a velocity measure is related to the size of impulse that could be sustained without failure since engineering systems may be subjected to pulse loads of finite duration attention is given to both the absolute and transient basin boudaries the significant erosion of these at homoclinic tangencies is particularly highlighted in the present study the fractal basins having a severely reduced integrity under all three criteria

rotating solutions and stability of parametric pendulum by perturbation method abstract rotating solutions of a parametrically driven pendulum are studied via a perturbation method by assuming the undamped unforced hamiltonian case as basic solution and damping and excitation as small perturbations the existence and stability of the harmonic solution are determined analytically first order terms are mainly considered but the extensions to higher order terms as well as to subharmonic rotations are straightforward setting up the analysis in the phase space instead of in the physical space has facilitated development of simple but comprehensive formulas comparison with numerical simulations shows that the analytical results are very effective in accurate predictions even for fairly large amplitudes and in detecting the saddle node bifurcation where the rotating solution is born a limited accuracy is observed to first order in detecting the period doubling bifurcation where it loses stability and an explanation is proposed

regularity and estimates for j holomorphic discs attached to a maximal totally real submanifold we prove that pseudo holomorphic discs attached to a maximal totally real submanifold inherit their regularity to the boundary from the regularity of the submanifold and of the almost complex structure the proof is based on the computation of an explicit lower bound for the kobayashi metric in almost complex manifolds which also yields explicit estimates of holderian norms of such discs

homotopy equivalence of nearby lagrangians and the serre spectral sequence we construct using relatively basic techniques a spectral sequence for exact lagrangians in cotangent bundles similar to the one constructed by fukaya seidel and smith that spectral sequence was used to prove that exact relative spin lagrangians in simply connected cotangent bundles with vanishing maslov class are homology equivalent to the base a similar result was also obtained by nadler the ideas in that paper were extended by abouzaid who proved that vanishing maslov class alone implies homotopy equivalence in this paper we present a short proof of the fact that any exact lagrangian with vanishing maslov class is homology equivalent to the base and that the induced map on fundamental groups is an isomorphism when the fundamental group of the base is pro finite this implies homotopy equivalence

convergence of yang mills higgs fields in this paper we study the convergence of yang mills higgs ymh fields defined on fiber bundles over riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the underlying surface is allowed to vary we show that away from the nodes the ymh fields converges up to gauge to a smooth ymh field modulo finitely many harmonic spheres while near the nodes where the conformal structure degenerates the ymh fields converges to a pair consisting of a flat connection and a twisted geodesic with potential in particular we generalize the recent compactness results on both harmonic maps from surfaces and twisted holomorphic curves to general ymh fields

experimental versus theoretical robustness of rotating solutions in a parametrically excited pendulum a dynamical integrity perspective the objective of this paper is showing how global safety arguments can be fruitfully used to interpret experimental results of a pendulum parametrically excited by wave motion in fact the results of an experimental campaign developed with the aim of simulating sea waves energy production by a parametric pendulum show that rotations exist in a region which is smaller than the theoretical one this discrepancy can be partially attributed to the experimental approximations and constraints but it has a deeper theoretical motivation by comparing the experimental results with the dynamical integrity profiles we have found that experimental rotations exist only where a measure of dynamical integrity accounting for both attractor robustness and basin compactness is large enough so that they can support experimental imperfections leading to changes in initial conditions

on the perturbation of the stationary discs in almost complex manifolds abstract we study the neighborhood of an embedded j holomorphic disc f attached along its boundary to a strictly pseudoconvex domain r 4 j in particular we give sufficient conditions for the set of all nearby attached j holomorphic discs to be a manifold

a burns krantz type theorem for domains with corners in their pioneering paper bk94 burns andkrantzhave established a boundary version of the classical cartan s uniqueness theorem if f is holomorphic self map of a smoothly bounded strongly pseudoconvex domain d c such that f z z o z p 3 as z p for some p d then f z z furthermore they give an example showing that the exponent 3 in the above statement cannot be decreased the goal of this paper is twofold first to give purely local boundary uniqueness results for maps defined only on one side as germs at a boundary point and hence not necessarily sending any domain to itself and also under the weaker assumption that f z z o z p 3 holds only for z in a proper cone in d with vertexp such results have no analogues in one complex variable in contrast with the situation when a domain is preserved our second goal is to extend the above results from boundaries of domains to real submanifolds m c of higher codimension recall that m is called generic if its tangent space tpm at every point p m spans tpc over c i e tpc n tpm itpm here the usual replacement for a one sided neighborhood of a boundary point is a wedge with edgem at a pointp m in the direction of an open cone npm tpc tpm i e a domain w c such that for any pair of open cones npm with 0 and 0 there exists a neighborhood u of p in c such that m u u w and m u u contains a neighborhood of p in w where we identify npm with a fixed complement of tpm in tpc c furthermore we extend the notion of strong pseudoconvexity to wedges as follows we call a wedge w with edge m at p in the direction of strongly

characterization in bi parameter space of a non ideal oscillator abstract we investigate the dynamical behavior of a non ideal duffing oscillator a system composed of a mass spring pendulum driven by a dc motor with limited power supply to identify new features on duffing oscillator parameter space due to the limited power supply we provide an extensive numerical characterization in the bi parameter space by using lyapunov exponents following this procedure we identify remarkable new organized distribution of periodic windows the ones known as arnold tongues and also shrimp shaped structures in addition we also identify intertwined basins of attraction for coexisting multiple attractors connected with tongues

multifractal fourier detrended cross correlation analysis of traffic signals abstract multifractal detrended cross correlation analysis mf dxa has been developed to detect the long range power law cross correlation of considered signals in the presence of non stationarity however crossovers arising from extrinsic periodic trends make the scaling behavior difficult to analyze we introduce a fourier filtering method to eliminate the trend effects and systematically investigate the multifractal cross correlation of simulated and real traffic signals the crossover locations are found approximately corresponding to the periods of underlying trend traffic velocity on one road and flows on adjacent roads show strong cross correlation they also present weak multifractality after periodic trends are removed the traffic velocity and flow are cross correlated in opposite directions which is accordant to their actual evolution

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

topological analysis and synthesis of chaotic time series abstract we have developed a topological procedure for analyzing chaotic time series which identifies the stretching and squeezing mechanisms responsible for chaotic behavior in low dimensional dynamical systems these mechanisms quantitatively described by a template or knot holder can then be used to model the processes which generate the original chaotic data set

practical method for determining the minimum embedding dimension of a scalar time series abstract a practical method is proposed to determine the minimum embedding dimension from a scalar time series it has the following advantages 1 does not contain any subjective parameters except for the time delay for the embedding 2 does not strongly depend on how many data points are available 3 can clearly distinguish deterministic signals from stochastic signals 4 works well for time series from high dimensional attractors 5 is computationally efficient several time series are tested to show the above advantages of the method

stationary holomorphic discs and finite jet determination problems we construct a family of small analytic discs attached to levi non degenerate hypersurfaces in mathbb c n 1 which is globally biholomorphically invariant we then apply this technique to study unique determination problems along levi non degenerate hypersurfaces that are merely of class mathcal c 4 this method gives 2 jet determination results for germs of biholomorphisms cr diffeomorphisms as well as in the almost complex setting

identifying evaluating and controlling dynamical integrity measures in non linear mechanical oscillators the erosion curves for the helmholtz the duffing and rigid block oscillators are constructed to investigate the loss of integrity in different mechanical systems various definitions of safe basin and integrity measures are reviewed compared with each other and applied to the considered cases a control method aimed at shifting the erosion profiles towards larger excitation amplitudes is considered too and its main features are discussed in depth

an existence theorem for stationary discs in almost complex manifolds an existence theorem for stationary discs of strongly pseudo convex domains in almost complex manifolds is proved more precisely it is shown that for all points of a suitable neighborhood of the boundary and for any vector belonging to certain open subsets of the tangent spaces there exists a unique stationary disc passing through that point and tangent to the given vector this result gives a generalization of a theorem of b coupet h gaussier and the second author originally proved only for almost complex structures which are small deformations of an integrable one

extremal discs and the regularity of cr mappings in higher codimension we develop a local theory of extremal analytic discs attached to a strictly pseudoconvex manifold of higher codimension in complex space we then apply the results to prove the regularity of cr homeomorphisms of such manifolds introduction in his celebrated paper lempert li introduced extremal analytic discs as geodesies of the kobayashi metric on a convex domain d c cn let a be the unit disc in the complex plane an analytic disc a d is called extremal if 0 attains its maximum among all analytic discs in d with the same values and directions at 0 g a extremal discs are important holomorphic invariants of d their boundaries lie in the boundary bd of the domain and form an invariant family of curves for the cr structure of bd lempert li l2 applies the extremal discs to the regularity of biholomorphic mappings monge amp re equations and normal forms of convex domains other applications include deformations and embeddibility of cr structures bl bd and polynomial hulls s

initiation and directional control of period 1 rotation for a parametric pendulum we study a time delayed feedback control for initiating period 1 rotations of a vertically excited parametric pendulum from arbitrary initial conditions the possibility of controlling the direction of rotation has also been explored we start with a simple linear time delayed control for which the control gain corresponding to the most stable period 1 rotation has been obtained using the floquet theory this control increases the basins of attraction of rotations but they do not encompass the full initial condition space we modify our control law by using a switched control gain that destabilizes all the oscillatory solutions and the entire initial condition space becomes the basin of attraction of either the clockwise or the anticlockwise rotation by a suitable modification of the switching condition we can choose a preferential stable direction of rotation hence we can initiate either clockwise or anticlockwise rotation for a parametric pendulum from arbitrary initial conditions performance of our controller in achieving this objective has been demonstrated for different sets of parameters to establish its effectiveness

analysis of economic growth fluctuations based on eemd and causal decomposition abstract in this paper we first apply ensemble empirical mode decomposition eemd to analyze the change rate of gdp time series for ten major countries each signal is decomposed into four modes with different scales and a residual trend the variance contribution and averaged period cycle for each mode is then calculated results show that economic growth fluctuations for most of the countries mainly fluctuate at a short period between 3 5 years then the causal decomposition proposed by yang et al is utilized to detect the mutual causation among different countries the novelty of this method is that the causal interaction is identified in instantaneous phase coherence at a specific time scale the strengths and directions of causal relationship for each mode among countries differ from each other which mirrors the fact that the world economic activities are fluctuated and changeable over varying periods however no visible causation for the fourth mode long term cycle among countries is characterized meaning that the development of economy over a long period for most countries depends on its own conditions

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

a weighted network evolution with traffic flow in this paper we propose a simple weighted network model that generalizes the complex network model evolution with traffic flow previously presented to investigate the relationship between traffic flow and network structure in the model the nodes in the network are represented by the traffic flow states the links in the network are represented by the transform of the traffic flow states and the traffic flow transported when performing the transform of the traffic flow states is considered as the weight of the link several topological features of this generalized weighted model such as the degree distribution and strength distribution have been numerically studied a scaling behavior between the strength and degree s klogks klogk is obtained by introducing some constraints to the generalized weighted model we study its subnetworks and find that the scaling behavior between the strength and degree is conserved though the topology properties are quite sensitive to the constraints

solvability of dirac type equations abstract this paper develops a weighted l 2 method for the half dirac equation for dirac bundles over closed riemann surfaces we give a sufficient condition for the solvability of the half dirac equation in terms of a curvature integral applying this to the dolbeault dirac operator we establish an automatic transversality criteria for holomorphic curves in kahler manifolds on compact riemannian manifolds we give a new perspective on some well known results about the first eigenvalue of the dirac operator and improve the estimates when the dirac bundle has a z 2 grading on riemannian manifolds with cylindrical ends we obtain solvability in the l 2 spaces with suitable exponential weights while allowing mild negativity of the curvature

polyfolds cobordisms and the strong weinstein conjecture abstract we prove the strong weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres

tight not semi fillable contact circle bundles extending our earlier results we prove that certain tight contact structures on circle bundles over surfaces are not symplectically semi fillable thus confirming a conjecture of ko honda

polynomial hulls with convex fibers and complex geodesics let x be a compact subset of z 1 cn with convex fibers several equivalent conditions are obtained that characterize polynomially convex hulls y x with nonempty interior under the latter assumption it is shown that every z0 w0 y and such that z0 1 is contained in a closed n dimensional complex submanifold of d cn which is tangent to y along an analytic disc we show as an application that some results of lempert on complex geodesies in convex domains are direct consequences of properties of polynomial hulls

fefferman s mapping theorem on almost complex manifolds in complex dimension two we give a necessary and sufficient condition for the smooth extension of a diffeomorphism between smooth strictly pseudoconvex domains in four real dimensional almost complex manifolds see theorem 1 1 the proof is mainly based on a reflection principle for pseudoholomorphic discs on precise estimates of the kobayashi royden infinitesimal pseudometric and on the scaling method in almost complex manifolds

recurrence plot based measures of complexity and their application to heart rate variability data the knowledge of transitions between regular laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems while several linear approaches are often insufficient to describe such processes there are several nonlinear methods that however require rather long time observations to overcome these difficulties we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data for the logistic map these measures enable us not only to detect transitions between chaotic and periodic states but also to identify laminar states i e chaos chaos transitions the traditional recurrence quantification analysis fails to detect the latter transitions applying our measures to the heart rate variability data we are able to detect and quantify the laminar phases before a life threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event our findings could be of importance for the therapy of malignant cardiac arrhythmias

recurrence plot statistics and the effect of embedding abstract recurrence plots provide a graphical representation of the recurrent patterns in a timeseries the quantification of which is a relatively new field here we derive analytical expressions which relate the values of key statistics notably determinism and entropy of line length distribution to the correlation sum as a function of embedding dimension these expressions are obtained by deriving the transformation which generates an embedded recurrence plot from an unembedded plot a single unembedded recurrence plot thus provides the statistics of all possible embedded recurrence plots if the correlation sum scales exponentially with embedding dimension we show that these statistics are determined entirely by the exponent of the exponential this explains the results of iwanski and bradley j s iwanski e bradley recurrence plots of experimental data to embed or not to embed chaos 8 1998 861 871 who found that certain recurrence plot statistics are apparently invariant to embedding dimension for certain low dimensional systems we also examine the relationship between the mutual information content of two timeseries and the common recurrent structure seen in their recurrence plots this allows time localized contributions to mutual information to be visualized this technique is demonstrated using geomagnetic index data we show that the au and al geomagnetic indices share half their information and find the timescale on which mutual features appear

jet determination of smooth cr automorphisms and generalized stationary discs we prove finite jet determination for finitely smooth cr diffeomorphisms of finitely smooth levi degenerate hypersurfaces in mathbb c n 1 by constructing generalized stationary discs glued to such hypersurfaces

monge ampere equations and moduli spaces of manifolds of circular type abstract a bounded manifold of circular type is a complex manifold m of dimension n admitting a bounded exhaustive real function u defined on m minus a point x o so that a it is a smooth solution on m x o to the monge ampere equation d d c u n 0 b x o is a singular point for u of logarithmic type and e u extends smoothly on the blow up of m at x o c d d c e u 0 at any point of m x o this class of manifolds naturally includes all smoothly bounded strictly linearly convex domains and all smoothly bounded strongly pseudoconvex circular domains of c n a set of modular parameters for bounded manifolds of circular type is considered in particular for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form it is also shown that the class of normalizing maps for an n dimensional manifold m is a new holomorphic invariant with the following property it is parameterized by the points of a finite dimensional real manifold of dimension n 2 when m is a non convex circular domain while it is of dimension n 2 2 n when m is a strictly linearly convex domain new characterizations of the circular domains and of the unit ball are also obtained

a c 2 smooth counterexample to the hamiltonian seifert conjecture in r 4 we construct a proper c 2 smooth function on r 4 such that its hamiltonian flow has no periodic orbits on at least one regular level set this result can be viewed as a c 2 smooth counterexample to the hamiltonian seifert conjecture in dimension four

use of recurrence plot and recurrence quantification analysis in taiwan unemployment rate time series abstract the aim of the article is to answer the question if the taiwan unemployment rate dynamics is generated by a non linear deterministic dynamic process this paper applies a recurrence plot and recurrence quantification approach based on the analysis of non stationary hidden transition patterns of the unemployment rate of taiwan the case study uses the time series data of the taiwan s unemployment rate during the period from 1978 01 to 2010 06 the results show that recurrence techniques are able to identify various phases in the evolution of unemployment transition in taiwan

stationary discs and finite jet determination for cr mappings in higher codimension abstract we discuss stationary discs for generic cr manifolds and apply them to the problem of finite jet determination for cr mappings we prove that a c 2 smooth cr diffeomorphism of two c 4 smooth strictly pseudoconvex levi generating cr manifolds is uniquely determined by its 2 jet at a given point a new key element of the proof is the existence of non defective stationary discs

the maslov class of the lagrange surfaces and gromov s pseudo holomorphic curves for an immersed lagrange submanifold w c t x one can define a nonnegative integer topologic invariant m w such that the image of h1 w z under the maslov class is equal to m w z in this paper the value of m w is calculated for the case of a two dimensional oriented manifold x with the universal cover homeomorphic to r2 and an embedded lagrange torus w it is proved that if x t2 and w is homologic to the zero section then m w 0 in all the other cases m w 2 the last result is true also for a wide class of oriented properly embedded lagrange surfaces in t r the proof is based on the gromov s theory of pseudo holomorphic curves some applications to the hamiltonian mechanics are mentioned

detecting intrinsic dynamics of traffic flow with recurrence analysis and empirical mode decomposition abstract in this paper we apply the empirical mode decomposition emd method to the recurrence plot rp and recurrence quantification analysis rqa to evaluate the frequency and time evolving dynamics of the traffic flow based on the cumulative intrinsic mode functions extracted by the emd the frequency evolving rp regarding different oscillation of modes suggests that apparent dynamics of the data considered are mainly dominated by its components of medium and low frequencies while severely affected by fast oscillated noises contained in the signal noises are then eliminated to analyze the intrinsic dynamics and consequently the denoised time evolving rqa diversely characterizes the properties of the signal and marks crucial points more accurately where white bands in the rp occur whereas a strongly qualitative agreement exists between all the non denoised rqa measures generally the emd combining with the recurrence analysis sheds more reliable abundant and inherent lights into the traffic flow which is meaningful to the empirical analysis of complex systems

a property of the functions and distributions annihilated by a locally integrable system of complex vector fields page introduction 387 1 basic notation and ingredients 389 2 approximation and constancy on the fibers of the classical solutions of the homogeneous equations 393 3 first consequences and interpretation of the fundamental theorem 398 4 distribution solutions of the homogeneous equations 402 5 regularity of the solutions of the homogeneous equations 409 6 example of a system that is analytic hypo elliptic but not co hypo elliptic 413 references 420

existence and classification of overtwisted contact structures in all dimensions we establish a parametric extension h principle for overtwisted contact structures on manifolds of all dimensions which is the direct generalization of the 3 dimensional result from 12 it implies in particular that any closed manifold admits a contact structure in any given homotopy class of almost contact structures

stationary discs glued to a levi non degenerate hypersurface we obtain an explicit parametrization of stationary discs glued to some levi non degenerate hypersurfaces these discs form a family which is invariant under the action of biholomorphisms we use this parametrization to construct a local circular representation of these hypersurfaces as a corollary we get the uniqueness of biholomorphisms with given 1 jet at some convenient point

on the geometry of model almost complex manifolds with boundary we study some special almost complex structures on strictly pseudoconvex domains in 2n they appear naturally as limits under a nonisotropic scaling procedure and play a role of model objects in the geometry of almost complex manifolds with boundary we determine explicitely some geometric invariants of these model structures and derive necessary and sufficient conditions for their integrability as applications we prove a boundary extension and a compactness principle for some elliptic diffeomorphisms between relatively compact domains

examples of symplectic structures in this paper we construct symplectic forms tilde omega k k geqq 0 on a compact manifold tilde y which have the same homotopy theoretic invariants but which are not diffeomorphic

periodic fourth order cubic nls local well posedness and non squeezing property abstract in this paper we consider the cubic fourth order nonlinear schrodinger equation 4nls under the periodic boundary condition we prove two results one is the local well posedness in h s t with 1 3 s 0 for the cauchy problem of the wick ordered 4nls the other one is the non squeezing property for the flow map of 4nls in the symplectic phase space l 2 t to prove the former we used the ideas introduced in 36 and 27 and to prove the latter we used the ideas in 8

scaling laws of the network traffic flow in this work a type of the evolution network is constructed in the evolution process of traffic flow we study the influence of the traffic dynamics on the structural properties of the evolution network and measure the probability distributions and scaling properties of the network the traffic dynamics is simulated by using the city traffic model i e the modified chsch model see e brockfeld r barlovic a schadschneider m schreckenberg phys rev e 64 2001 056132 the topological structure of the evolution network is strongly related to the traffic dynamics and various distributions of the connections can be found under different traffic conditions

hamiltonian collapsing of irrational lagrangian submanifolds with small first betti number among the main symplectic invariants of a closed lagrange submanifoldl of the cotangent of n is the tubular radiusr l defined as the smallest tube d r n 1 of n t n in whichl can be pushed by an hamiltonian diffeotopy of n we show here using pseudo holomorphic techniques that such a submanifold cannot collapse if the first betti number ofl is smaller than 3 and if the maslov class ofl does not vanish in other words r l is then strictly positive and one can actually give an explicit lower bound in terms of the liouville and maslov classes ofl

moduli for pointed convex domains a moduli space for the class of pointed strictly linearly convex domains in n is obtained it is shown that the space of pointed smoothly bounded strictly linearly convex domains with a fixed indicatrix is parameterized by a class of deformations of the cr structure of the boundary of the indicatrix these deformations are constructed by using the circular representation of a domain to pull back its complex structure tensor to the indicatrix a careful study of the pull back structure shows that the allowable deformations are parameterized by a class of complex hamiltonian vector fields the proof of this fact is based on the folland stein estimates for the bar partial b complex of the boundary of the indicatrix