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
• Texto completo no disponible (Saber más ...)
• 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.