15 novembre 2013

Formes normales résonantes pour des Hamiltoniens non analytiques

22 novembre 2013

Jean-Pierre MARCO :
Orbites de diffusion pour des polysystèmes de correspondances sur l'anneau

29 novembre 2013

Marcel GUARDIA :
Exponentially small splitting of separatrices for one and a half degree of freedom Hamiltonian Systems close to a resonance

Abstract: We consider nearly integrable Hamiltonian Systems of one and a  half degree of freedom close to a simple resonance. It is a well known  fact that generically in the resonance there appear hyperbolic periodic orbits whose stable and unstable invariant manifolds intersect transversaly. Nevertheless, the transversality of this intersection is exponentially small with respect to the perturbation parameter and, therefore, Melnikov Theory cannot be applied to obtain quantitative measures of this splitting. In this talk we provide an asymptotic formula for the splitting, which generically differs from what Melnikov Theory predicts.