American Institute of Mathematical Sciences

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

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

Ernest Fontich 1, , Rafael de la Llave 2, and  Yannick Sire 3,

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, United States
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, Russian Federation

Received  October 2008 Revised  February 2009 Published  May 2009

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.
Keywords: coupled oscillators., Whiskered tori, quasi-periodic breathers, Hamiltonian systems, quasi-periodic solutions.
Mathematics Subject Classification: Primary: 37J40; Secondary: 37K55, 37K60, 70H0.
Citation: Ernest Fontich, Rafael de la Llave, Yannick Sire. A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems. Electronic Research Announcements, 2009, 16: 9-22. doi: 10.3934/era.2009.16.9
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