Fulltext

Localized Stable Manifolds for Whiskered Tori in Coupled Map Lattices with Decaying Interaction

Blazevski, Daniel ; de la Llave, Rafael

In: Annales Henri Poincaré, 2014, vol. 15, no. 1, p. 29-60

Ajouter à la liste personnelle
    Titre
    • Localized Stable Manifolds for Whiskered Tori in Coupled Map Lattices with Decaying Interaction
    Auteur
    • Blazevski, Daniel. Department of Mechanical and Process Engineering, Institute for Mechanical Systems, ETH Zurich, Tannenstrasse 3, 8092, Zurich, Switzerland
    • de la Llave, Rafael. School of Mathematics, Georgia Institute of Technology, 686 Cherry St, 30332, Atlanta, GA, USA
    Type de document
    • Postprint
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:326382
    Summary
    In this paper we consider lattice systems coupled by local interactions. We prove invariant manifold theorems for whiskered tori (we recall that whiskered tori are quasi-periodic solutions with exponentially contracting and expanding directions in the linearized system). The invariant manifolds we construct generalize the usual (strong) (un)stable manifolds and allow us to consider also non-resonant manifolds. We show that if the whiskered tori are localized near a collection of specific sites, then so are the invariant manifolds. We recall that the existence of localized whiskered tori has recently been proven for symplectic maps and flows in Fontich etal. (J Diff Equ, 2012), but our results do not need that the systems are symplectic. For simplicity we will present first the main results for maps, but we will show that the result for maps imply the results for flows. It is also true that the results for flows can be proved directly following the same ideas.