How to increase the energy (in a geodesic flow) with a small (quasiperiodic) forcing

Amadeu Delshams ^[1] ; Rafael de la Llave ^[2] ; Tere M. Seara ^[1]
1. [1] Universitat Politècnica de Catalunya
  
  Universitat Politècnica de Catalunya
  
  Barcelona, España
2. [2] University of Texas at Austin
  
  University of Texas at Austin
  
  Estados Unidos
Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals , Anastasio Pedro Santos Yanguas , 2001, ISBN 8469961446, págs. 517-518
Idioma: inglés
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Resumen
- In this work we will describe the proof of the result that Hamiltonian systems consisting on a geodesic flow in some manifolds, verifying certain hypotheses, and perturbed by a quasi-periodic potential, have orbits of unbounded energy. We will assume that the frequency of the perturbation satisfies some Diophantine conditions, that the metric and the external perturbation are smooth enough, that the geodesic flow satisfies some mild hyperbolicity conditions and that the external potential satisfies some non-degeneracy conditions.