A method for the study of whiskered quasi-periodic andalmost-periodic solutions in finite and infinite dimensionalHamiltonian systems

Ernest Fontich; Rafael de la Llave; Yannick Sire

doi:10.3934/era.2009.16.9

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2009, Volume 16: 9-22. Doi: 10.3934/era.2009.16.9

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A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems

1.
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona
2.
School of Mathematics, Georgia Institute of Technology, 686 Cherry St., Atlanta, GA 30332-0160
3.
Laboratoire LATP CNRS, Université Paul Cézanne Aix-Marseille 3, 13397 Marseille Cedex 20, France and Laboratoire Poncelet, UMI 2615, 119002, Bolshoy Vlasyevskiy Pereulok 11, Moscow

Received: September 30, 2008

Revised: January 31, 2009

Published: December 2008

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Abstract

We describe a method to study the existence of whiskered quasi-periodic solutions in Hamiltonian systems. The method applies to finite dimensional systems and also to lattice systems and to PDE's including some ill posed ones. In coupled map lattices, we can also construct solutions of infinitely many frequencies which do not vanish asymptotically.

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Mathematics Subject Classification: Primary: 37J40; Secondary: 37K55, 37K60, 70H08.

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A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems

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