15 novembre 2013
Abed BOUNEMOURA :
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.