Continuation of relative periodic orbits in a class of triatomic hamiltonian systems
Families of whiskered tori for a-priori stable/unstable Hamiltonian systems and construction of unstable orbits.
Generic Nekhoroshev theory without small divisors
In this article, we present a new approach of Nekhoroshev’s theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak, it combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of...
Linearization of nonholonomic systems at equilibrium points.
On stability zones for discrete-time periodic linear Hamiltonian systems.
On the optimality of double-bracket flows.
Quadratic and homogeneous Hamilton-Poisson systems on .
Stability is not open
We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.
Stability of a time discrete perturbed dynamical systems with delay.
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...
The direct Lyapunov method for an almost periodic difference system on a compactum.