fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain abstract uniform energy and l 2 decay of solutions for linear wave equations with localized dissipation will be given in order to derive the l 2 decay property of the solution a useful device whose idea comes from ikehata matsuyama sci math japon 55 2002 33 is used in fact we shall show that the l 2 norm and the total energy of solutions respectively decay like o 1 t and o 1 t 2 as t for a kind of the weighted initial data

hofer s question on intermediate symplectic capacities roughly twenty five years ago hofer asked can the cylinder b 2 1 times mathbb r 2 n 1 be symplectically embedded into b 2 n 1 r times mathbb r 2 for some r 0 we show that this is the case if r geq sqrt 2 n 1 2 n 2 2 we deduce that there are no intermediate capacities between 1 capacities first constructed by gromov in 1985 and n capacities answering another question of hofer in 2008 guth reached the same conclusion under the additional hypothesis that the intermediate capacities should satisfy the exhaustion property

local existence of solutions for the initial boundary value problem of the nonlinear elastodynamic system outside a domain abstract in this paper we deal with the mixed initial boundary value problem of dirichlet type for the nonlinear elastodynamic system outside a domain the local existence of solutions to this problem is proved by iteration

symplectic topology and hamiltonian dynamics on etudie des applications symplectiques non lineaires capacites symplectiques construction d une capacite symplectique problemes de plongement problemes de rigidite

energy decay rates of elastic waves in unbounded domain with potential type of damping abstract in this paper we first show that the total energy of solutions for a semilinear system of elastic waves in r n with a potential type of damping decays in an algebraic rate to zero we study the critical potential case and we assume that the initial data have a compact support an application for the euler poisson darboux type dissipation v t x is obtained and in this case the compactness of the support on the initial data is not necessary finally we shall discuss the energy concentration region for the linear system of elastic waves in an exterior domain

a geometric obstruction to the contact type property prompted by the existence results for periodic orbits on energy surfaces in 1979 a weinstein introduced the following concept we2 let m be a symplectic manifold i e a manifold m of even dimension 2n with a nondegenerate closed 2 form a hypersurface s m throughout this paper all hypersurfaces are assumed to be smooth without boundary is said to be of contact type if there exists a 1 form on s such that i d s and ii d n 1 is a volume form on s

on the escape rate from a metastable state in a nonpotential system abstract the escape rate from a metastable state is computed for a nonpotential system described by a general multivariate fokker planck equation the result is a generalization of the escape rate obtained by other authors in the case of potential systems a straightforward application is found in the derivation of the grote hynes result for chemical rates in solution another characteristic application is the theory of nucleation in nonlinear chemical systems far from equilibrium which has been developed in a previous paper of the authors without a proper derivation of the nucleation rate formula j stat phys 50 1988 935

entropy extropy and information potential in stochastic systems far from equilibrium the relations between information entropy and energy which are well known in equilibrium thermodynamics are not clear far from equilibrium moreover the usual expression of the classical thermodynamic potentials is only valid near equilibrium in previous publications we showed for a chemical system maintained far from equilibrium that a new thermodynamic potential the information potential can be de4ned by using the stochastic formalism of the master equation here we extend this theory to a completely general discrete stochastic system for this purpose we use the concept of extropy which is de4ned in classical thermodynamics as the total entropy produced in a system and in the reservoirs during their equilibration we show that the statistical equivalent of the thermodynamic extropy is the relative information if a coarse grained description by means of the thermodynamic extensive variables is available which is the case for many macroscopic systems the coarse grained statistical extropy allows one to de4ne the information potential in the thermodynamic limit using this potential we study the evolution of such systems towards a non equilibrium stationary state we derive a general thermodynamic inequality between energy dissipation and information dissipation which sharpens the law of the maximum available work for non equilibrium systems c 2002 published by elsevier science b v

symplectic rigidity symplectic fixed points and global perturbations of hamiltonian systems in this paper we study a generalized symplectic fixed point problem first considered by j moser in 20 from the point of view of some relatively recently discovered symplectic rigidity phenomena this problem has interesting applications concerning global perturbations of hamiltonian systems 2007 wiley periodicals inc

decay of solutions for a semilinear system of elastic waves in an exterior domain with damping near infinity abstract we show that the solutions of a semilinear system of elastic waves in an exterior domain with a localized damping near infinity decay in an algebraic rate to zero we impose an additional condition on the lame coefficients it seems that this restriction cannot be overcome by using the two finite speed propagation of the elastic model since we do not assume compact support on the initial data and because the dissipation does not have compact support the decay rates obtained for the total energy of the linear problem and the l 2 norm of the solution improve previous results for the semilinear problem the decay rates in this paper seem to be the first contribution mainly in the context of initial data without compact support and localized dissipation

irreversibility and fluctuation theorem in stationary time series the relative entropy between the joint probability distribution of backward and forward sequences is used to quantify time asymmetry or irreversibility for stationary time series the parallel with the thermodynamic theory of nonequilibrium steady states allows us to link the degree of asymmetry in the time signal with the distance from equilibrium and the lack of detailed balance among its states we study the statistics of time asymmetry in terms of the fluctuation theorem showing that this type of relationship derives from simple general symmetries valid for any stationary time series

metastable lifetime for a class of chemical systems near criticality abstract we consider a n dimensional autocatalytic chemical system with a finite metastable state which tends to become critical away from the critical situation the relaxation time from the metastable state to the final absorbing state can be computed by using inverse of the stationary probability distribution of the system at its minimal value it is difficult to obtain explicit results on the stationary probability distribution in general for several variables nevertheless we can estimate this quantity near criticality and we show that its critical exponent is 2 under rather general conditions this result is verified explicitly on an example for which a direct calculation can be done

dissipative structure and diffusion phenomena for doubly dissipative elastic waves in two space dimensions abstract in this paper we study the cauchy problem for doubly dissipative elastic waves in two space dimensions where two different damping terms consist of friction or structural damping we derive energy estimates and diffusion phenomena with different assumptions on initial data particularly we find a new threshold for the influence from different damping on diffusion phenomena additionally optimal decay estimates of solution from the above and the below in a weighted l 1 framework are obtained

interaction of a hopf bifurcation and a symmetry breaking bifurcation stochastic potential and spatial correlations the multivariate master equation for a general reaction diffusion system is solved perturbatively in the stationary state in a range of parameters in which a symmetry breaking bifurcation and a hopf bifurcation occur simultaneously thestochastic potential u is in general not analytic however in the vicinity of the bifurcation point and under precise conditions on the kinetic constants it is possible to define a fourth order expansion ofu around the bifurcating fixed point under these conditions the domains of existence of different attractors including spatiotemporal structures as well as the spatial correlations of the fluctuations around these attractors are determined analytically the role of fluctuations in the existence and stability of the various patterns is pointed out

a new method of analysis of the effect of weak colored noise in nonlinear dynamical systems a systematic method for obtaining the asymptotic behavior of a dynamical system forced by colored noise in the limit of small intensity is developed it is based on the search of wkb solutions to the fokker planck equation for the joint probability density of the system and noise in which the perturbation expansion is continued to the first correction beyond the hamilton jacobi limit the method can be applied to noise with correlation time of order unity it is illustrated on the normal form of a pitchfork bifurcation where it is pointed out that additive noise can induce a shift of the most probable value this prediction is confirmed by numerical simulation of the stochastic differential equations

quasipotentials for simple noisy maps with complicated dynamics the theory of nonequilibrium potentials or quasipotentials is a physically motivated approach to small random perturbations of dynamical systems leading to exponential estimates of invariant probabilities and mean first exit times in the present article we develop the mathematical foundation of this theory for discrete time systems following and extending the work of freidlin and wentzell and kifer we discuss strategies for calculating and estimating quasipotentials and show their application to one dimensionals unimodal maps the method proves to be especially suited for describing the noise scaling behavior of invariant probabilities e g for the map occurring as the limit of the feigenbaum period doubling sequence we show that the method allows statements about the scaling behavior in the case of localized noise too which does not originally lie within the scope of the quasipotential formalism

energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations we derive the total energy decay e t leq i 0 1 t 1 and l 2 boundedness u t 2 leq ci 0 for the solutions to the initial boundary value problem for the wave equation in an exterior domain omega u tt delta u a x u t 0 mbox in omega times 0 infty with u x 0 u 0 x u t x 0 u 1 x mbox and u partial omega 0 where i 0 u 0 h 1 u 1 2 and a x is a nonnegative function which is positive near some part of the boundary partial omega and near infinity we apply these estimates to prove the global existence of decaying solutions for semilinear wave equations with nonlinearity f u like u alpha u alpha 0 we note that no geometrical condition is imposed on the boundary partial omega

on the topological properties of symplectic maps in this paper we show that symplectic maps have surprising topological properties in particular we construct an interesting metric for the symplectic diffeomorphism groups which is related but not obviously to the topological properties of symplectic maps and phase space geometry we also prove a certain number of generalised symplectic fixed point theorems and give an application to a hamiltonian system

stochastic analysis of a hopf bifurcation master equation approach the effect of inhomogeneous fluctuations in a reaction diffusion system exhibiting a hopf bifurcation is analyzed using the master equation approach a taylor expansion of the logarithm of the stationary probability known as the stochastic potential is calculated this procedure displays marked analogies with the theory of normal forms the critical potential reduced to its local expansion around an arbitrary point of the limit cycle brings out the essential role played by the phase of the oscillating variables a comparison with the langevin analysis of walgraefet al j chem phys 78 6 3043 1983 is performed

the geometry of symplectic energy non squeezing theorem which says that it is impossible to embed a large ball symplectically into a thin cylinder of the form r2 x b2 where b2 is a 2 disc this led to hofer s discovery of symplectic capacities which give a way of measuring the size of subsets in symplectic manifolds recently hofer found a way to measure the size or energy of symplectic diffeomorphisms by looking at the total variation of their generating hamiltonians this gives rise to a bi invariant pseudo norm on the group ham m of compactly supported hamiltonian symplectomorphisms of the manifold m the deep fact is that this pseudo norm is a norm in other words the only symplectomorphism on m with zero energy is the identity map up to now this had been proved only for sufficiently nice symplectic manifolds and by rather complicated analytic arguments in this paper we consider a more geometric version of this energy which was first considered by eliashberg and hofer in connection with their study of the extent to which the interior of a region in a symplectic manifold determines its boundary we prove by a simple geometric argument that both versions of energy give rise to genuine norms on all symplectic manifolds roughly speaking we show that if there were a symplectomorphism of m which had too little energy one could embed a large ball into a thin cylinder m x

equality governing nonequilibrium fluctuations and its information theory and thermodynamic interpretations the master equation is cast in the form of an equality involving the variation in the course of a transformation of a quantity playing the role of a generalized potential weighted with the probability of allowable transformations emanating from different initial states in the most general case this equality cannot be formulated entirely in terms of thermodynamic variables and state functions some conditions under which such a reduction becomes possible are identified and a comparison with fluctuation and work type relationships previously reported in the literature is carried out

stochastic analysis of symmetry breaking bifurcations master equation approach the multivariate master equation for a general reaction diffusion system is solved perturbatively in the vicinity of a bifurcation point leading to symmetry breaking transitions the possibility to express the result through a brazovskii type of potential is examined and a comparison with the langevin analysis of walgraefet al adv chem phys 49 311 1982 is performed

periodic solutions on hypersurfaces and a result by c viterbo on considere un champ vectoriel hamiltonien x j h x x h x sur x r 2n h etant une fonction lisse dont le gradient h est defini par rapport a la metrique euclidienne on cherche des solutions periodiques sur une surface d energie donnee s x r 2n h x const supposee reguliere

the conley conjecture we prove the conley conjecture for a closed symplectically aspherical symplectic manifold a hamiltonian diffeomorphism of such a manifold has infinitely many periodic points more precisely we show that a hamiltonian diffeomorphism with finitely many fixed points has simple periodic points of arbitrarily large period this theorem generalizes for instance a recent result of hingston establishing the conley conjecture for tori

on the stationary distribution of self sustained oscillators around bifurcation points a double expansion in powers of the damping coefficient and noise intensity is shown to be a powerful method for obtaining the stationary distribution of systems that after rescaling become weakly damped conservative ones systems undergoing hopf bifurcations belong to this class as an illustrative example the generalized van der pol oscillator is considered around its bifurcation point a calculation is carried out up to third order in both the noise intensity and the bifurcation parameter damping coefficient

convex hamiltonian energy surfaces and their periodic trajectories in this paper we introduce symplectic invariants for convex hamiltonian energy surfaces and their periodic trajectories and show that these quentities satisfy several nontrivial relations in particular we show that they can be used to prove multiplicity results for the number of periodic trajectories

variational problems related to self similar solutions of the heat equation on demontre la compacite de certains plongements de sobolev sous de bonnes conditions sur les poids k x exp x c 2 r n r on considere des methodes variationnelles pour la resolution d equations elliptiques

intrinsic fluctuations in chaotic dynamics abstract the multivariate master equation of a chemical system exhibiting spatio temporal chaos is investigated it is shown that the probability distribution in the presence of fluctuations remains centered on the underlying deterministic attractor

lp lq estimates of solutions to the damped wave equation in 3 dimensional space and their application it has been asserted that the damped wave equation has the diffusive structure as t in this paper we consider the cauchy problem in 3 dimensional space for the linear damped wave equation and the corresponding parabolic equation and obtain the lp lq estimates of the difference of each solution which represent the assertion precisely explicit formulas of the solutions are analyzed for the proof the second aim is to apply the lp lq estimates to the semilinear damped wave equation with power nonlinearity if the power is larger than the fujita exponent then the time global existence of small weak solution is proved and its optimal decay order is obtained

the kunneth formula in floer homology for manifolds with restricted contact type boundary we prove the kunneth formula in floer co homology for manifolds with restricted contact type boundary we use viterbo s definition of floer homology involving the symplectic completion by adding a positive cone over the boundary the kunneth formula implies the vanishing of floer co homology for subcritical stein manifolds other applications include the weinstein conjecture in certain product manifolds obstructions to exact lagrangian embeddings existence of holomorphic curves with lagrangian boundary condition as well as symplectic capacities

global existence of solutions for semilinear damped wave equations in rn with noncompactly supported initial data abstract we consider the n dimensional cauchy problem in r n for a semilinear damped wave equation with a power type nonlinearity u p for a noncompactly supported initial data which has a small energy we shall derive a global in time existence result in the case when the power of the nonlinear term satisfies 1 2 n p n n 2 this generalizes a previous result due to todorova yordanov j differential equations 174 2001 464 489 which dealt with a solution in the framework of compactly supported initial data

nonequilibrium potentials near instabilities the existence of polynomial approximations for nonequilibrium potentials determined by a master equation near an instability of arbitrary codimension with diagonalizable linear part is studied it is shown that the approximations exist provided some relations are satisfied between the coefficients of the master equation

morse type index theory for flows and periodic solutions for hamiltonian equations an index theory for flows is presented which extends the classical morse theory for gradient flows on compact manifolds the theory is used to prove a morse type existence statement for periodic solutions of a time dependent periodic in time and asymptotically linear hamiltonian equation