Dynamical systems on lattices with decaying interaction. I: A functional analysis framework

DOI10.1016/J.JDE.2010.07.023zbMath1213.37114OpenAlexW1990590225MaRDI QIDQ631882

Rafael de la Llave, Pau Martín, Ernest Fontich

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.2010.07.023

zbMATH Keywords

weakly coupled systemsdynamical systems on lattices

Mathematics Subject Classification ID

Invariant manifold theory for dynamical systems (37D10) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60)

Related Items (6)

Dynamical systems on lattices with decaying interaction. II: Hyperbolic sets and their invariant manifolds ⋮ Invariant Objects on Lattice Systems with Decaying Interactions ⋮ 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 ⋮ Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices ⋮ Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto--Sivashinsky Equation

Cites Work

• Dynamical systems on lattices with decaying interaction. II: Hyperbolic sets and their invariant manifolds
• The imbedding problem for Riemannian manifolds
• Uniqueness of the SRB measure for piecewise expanding weakly coupled map lattices in any dimension
• Random fields
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Equilibrium measures for coupled map lattices: Existence, uniqueness and finite-dimensional approximations
• The entropy formula for SRB-measures of lattice dynamical systems
• Weakly connected neural networks
• Regularity of the composition operator in spaces of Hölder functions
• Smooth dependence of thermodynamic limits of SRB-measures
• Tutorials in mathematical biosciences. I: Mathematical neuroscience
• Sinai-Ruelle-Bowen measures for lattice dynamical systems
• Coupled map lattices without cluster expansion
• The Fermi-Pasta-Ulam problem. A status report
• Dynamics of coupled map lattices and of related spatially extended systems. Lectures delivered at the school-forum CML 2004, Paris, France, June 21 -- July 2, 2004.
• Traveling Waves of Bistable Dynamics on a Lattice
• The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
• Some physical models of the reaction-diffusion equation, and coupled map lattices
• Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
• Spacetime chaos in coupled map lattices
• Nonlinear dynamics and statistical physics of DNA
• Coupled analytic maps
• Equilibrium states for lattice models of hyperbolic type
• Transfer operators for coupled analytic maps
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Dynamical systems on lattices with decaying interaction. I: A functional analysis framework