Décomposition des difféomorphismes du tore en applications déviant la verticale (avec un appendice en collaboration avec Jean-Marc Gambaudo)
Density of chaotic dynamics in periodically forced pendulum-type equations
We announce that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics for a dense set of forcing terms in a space of periodic functions with zero mean value. The approach is based on global variational methods.
Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems
We consider the problem of Arnold’s diffusion for nearly integrable isochronous Hamiltonian systems. We prove a shadowing theorem which improves the known estimates for the diffusion time. We also justify for three time scales systems that the splitting of the separatrices is correctly predicted by the Poincaré-Melnikov function.