Amadeu DELSHAMS

Departament de Matematica Aplicada I
Universitat Politecnica de Catalunya
Diagonal 647, 08028 Barcelona 
Espagne
amadeu@ma1.upc.es

Perturbed ellipsoidal billiards (with Y.~Fedorov and R.~Ram{\'\i}rez-Ros)

Abstract : We consider perturbations of general ellipsoidal billiards as a paradigm of a nearly-integrable 4D-discrete Lagrangian system. In the integrable case, we give the explicit biasymptotic solutions and describe the corresponding asymptotic variety. The persistence of some of these biasymptotic solutions under perturbations is studied by means of the Melnikov potential. For non-trivial polynomial peturbations, the Melnikov potential is non-constant and the variety of biasymptotic solutions breaks up. Some examples with explicit computations are presented.