Jacky CRESSON

Equipe de Mathematiques de Besancon
CNRS-UMR 6623
Universite de Franche-Comte
16 route de Gray
25030 Besancon Cedex
France
cresson@math.jussieu.fr

Instability times along transition chain

Abstract : We discuss several geometrical methods to compute time of drift along transition chains. The first one, initiated by J.P. Marco used the Easton's windowing method. The second one is based on a new geometric tool called the transfer lemma and the proof of the transitivity property for Treshchev tori. The third one, is based on symbolic dynamics and periodic orbits for Treshchev tori with a transversal homoclinic connection. We prove that near a transition chain of Treshchev tori there exits a "dual" chain of periodic hyperbolic orbits. Then, we compute the time of instability along this chain.

These methods can be used to prove the Chirikov's conjecture about the optimality of the stability exponent of the Nekhoroshev theorem.