Jean-Pierre MARCO

Institut de Mathématiques de Jussieu.
Université Paris 6
Case 247
4 place Jussieu
75252 Paris cedex 05
marco@math.jussieu.fr
 

Dynamics in the vicinity of double resonances.

Abstract: We consider a near-integrable hamiltonian system and examine its behaviour near double resonances. An averaging allows to consider the system as a perturbation of the product of natural system on the cotangent bundle of the 2 torus and a trivial system. One can prove, under natural conditions, the existence of chains hyperbolic periodic orbits for the first system, and as a consequence after suspension and perturbation, the existence of orbits circulating around the double resonance.