Title:
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Dynamical systems on lattices with decaying interaction I: A functional analysis framework
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Author:
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Fontich, Ernest; Llave Canosa, Rafael de la; Martín de la Torre, Pablo
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
Abstract:
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We consider weakly coupled map lattices with a decaying interaction. That is, we consider systems which consist of a phase space
at every site such that the dynamics at a site is little affected by the dynamics at far away sites. We develop a functional analysis framework which formulates
quantitatively the decay of the interaction and is able to deal with lattices such that the sites are manifolds. This framework is very well suited to study systematically invariant objects. One obtains that the invariant objects are essentially local.
We use this framework to prove a stable manifold theorem and show that the manifolds are as smooth as the maps and have decay properties (i.e. the derivatives of one of the coordinates of the manifold with respect to the coordinates at far away sites are
small). Other applications of the framework are the study of the structural stability of maps with decay close to uncoupled possessing
hyperbolic sets and the decay properties of the invariant manifolds of their hyperbolic sets, in the companion paper by Fontich
et al. (2011) [10]. |
Abstract:
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Peer Reviewed |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals -Lattice dynamics -Weakly coupled systems -Reticles, Teoria de |
Rights:
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Document type:
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Article - Published version Article |
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