José Tomàs LAZÀRO

Dept. Matemàtica Aplicada i Telemàtica
Escola Universitària Politècnica
Av. Victor Balaguer, s/n
E-08800 Vilanova i la Geltru (Barcelona) 
Espagne
lazaro@mat.upc.es
 

Splitting in Reversible Systems (with Amadeu Delshams)

Abstract : We deal with reversible systems, i.e. systems invariant under a linear involution in the phase space and a reversion in the time parametrization. Our aim is to study the measure of the splitting of the separatrices of a paradigmatic example: a pendulum forced by a quasiperiodic, non-Hamiltonian, reversible perturbation. For this purpose, we present a convergent iterative scheme leading the perturbed reversible system to its Normal Form, by means of a sequence of suitable transformations, preserving reversibility and providing good estimates of the loss of domain in the angular variables.