Stability of a time discrete perturbed dynamical systems with delay.
Stability of Caustics.
Stability of closed characteristics on compact convex hypersurfaces in
Stability of higher order singular points of Poisson manifolds and Lie algebroids
We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first-order approximation (not necessarily linear) of a given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical Lichnerowicz-Poisson cohomology and the deformation cohomology for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide several examples of stable singular...
Stable norms of non-orientable surfaces
We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater than two.
Staircase baker's map generates flaring-type time series.
Star-products on symplectic manifolds
Statistics, yokes and symplectic geometry
Stochastic Stability in Some Chaotic Dynamical Systems.
Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles
This article is about almost reducibility of quasi-periodic cocycles with a diophantine frequency which are sufficiently close to a constant. Generalizing previous works by L.H. Eliasson, we show a strong version of almost reducibility for analytic and Gevrey cocycles, that is to say, almost reducibility where the change of variables is in an analytic or Gevrey class which is independent of how close to a constant the initial cocycle is conjugated. This implies a result of density, or quasi-density,...
Strong stochastic stability and rate of mixing for unimodal maps
Structure theory for second order 2D superintegrable systems with 1-parameter potentials.
Structures localemnt plates dans certaines variétés symplectiques.
Structures symplectiques faibles et intégrabilité globale de certains systèmes hamiltoniens
Structures symplectiques singulières génériques
Soit une variété différentiable de dimension paire munie d’une 2-forme différentielle fermée générique . L’apparition éventuelle d’un lieu de dégénérescence du rang de est l’obstacle à ce que soit une structure symplectique. Nous étudions les propriétés géométriques de et nous caractérisons l’algèbre des hamiltoniennes admissibles de i.e. les fonctions différentiables qui possèdent un champ hamiltonien sur .
Studies on the Painlevé Equations. III. Second and Fourth Painlevé Equations PII and PIV.
Subharmonic solutions of a nonconvex noncoercive hamiltonian system
In this paper we study the existence of subharmonic solutions of the hamiltonian systemwhere is a linear map, is a -function and is a continuous function.
Subharmonic solutions of a nonconvex noncoercive Hamiltonian system
In this paper we study the existence of subharmonic solutions of the Hamiltonian system where u is a linear map, G is a C1-function and e is a continuous function.
Summability of first integrals of a -non-integrable resonant Hamiltonian system
This article studies the summability of first integrals of a -non-integrable resonant Hamiltonian system. The first integrals are expressed in terms of formal exponential transseries and their Borel sums. Smooth Liouville integrability and a relation to the Birkhoff transformation are discussed from the point of view of the summability.
Superintegrability and time-dependent integrals
While looking for additional integrals of motion of several minimally superintegrable systems in static electric and magnetic fields, we have realized that in some cases Lie point symmetries of Euler-Lagrange equations imply existence of explicitly time-dependent integrals of motion through Noether’s theorem. These integrals can be combined to get an additional time-independent integral for some values of the parameters of the considered systems, thus implying maximal superintegrability. Even for...