Dynamical systems on lattices with decaying interaction. II: Hyperbolic sets and their invariant manifolds

DOI10.1016/J.JDE.2011.01.015zbMath1213.37115OpenAlexW2094250300MaRDI QIDQ631883

Pau Martín, Ernest Fontich, Rafael de la Llave

Publication date: 14 March 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.01.015

zbMATH Keywords

invariant manifoldsstructural stabilityhyperbolic setsshadowing lemmadynamical systems on lattices

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems with hyperbolic orbits and sets (37D05) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60)

Related Items (5)

Dynamical systems on lattices with decaying interaction. I: A functional analysis framework ⋮ Localized stable manifolds for whiskered tori in coupled map lattices with decaying interaction ⋮ Normal forms and Sternberg conjugation theorems for infinite dimensional coupled map lattices ⋮ Some breathers and multi-breathers for FPU-type chains ⋮ Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices

Cites Work

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• Dynamical systems on lattices with decaying interaction. I: A functional analysis framework
• Equilibrium measures for coupled map lattices: Existence, uniqueness and finite-dimensional approximations
• Smooth dependence of thermodynamic limits of SRB-measures
• On a theorem of Anosov
• Neighborhoods of hyperbolic sets
• The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
• Spacetime chaos in coupled map lattices
• Equilibrium states for lattice models of hyperbolic type

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