Teoría KAM sin coordenadas acción ángulo

A. Jorba ^[1] ; A. González ^[1] ; R. de la Llave ^[2] ; J. Villanueva ^[3]
1. [1] Universitat de Barcelona
  
  Universitat de Barcelona
  
  Barcelona, España
2. [2] University of Texas at Austin
  
  University of Texas at Austin
  
  Estados Unidos
3. [3] Universitat Politècnica de Catalunya
  
  Universitat Politècnica de Catalunya
  
  Barcelona, España
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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. 541-542
Idioma: español
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Resumen
- The classical KAM methods, strongly supported on the use of canonical trans- formations in the action-angle context, are not efficient to be applied to a wide range of systems in which the Hamiltonian is known (for instance) written in Cartesian coordinates. In this communication we present some ideas to deal with KAM theory using “parameterizations” instead of “transformations” and “graphs”, which we think is an efficient way to work with a more general class of Hamiltonian systems than the classical methods (in particular, for systems motivated by real world problems). With the present approach, we can extend several well-known results of KAM theory to these systems, even when the classical statements are difficult to be applied.