Equilibrium measures for coupled map lattices: Existence, uniqueness and finite-dimensional approximations

Miaohua Jiang, Yakov B. Pesin

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Abstract

We consider coupled map lattices of hyperbolic type, i.e., chains of weakly interacting hyperbolic sets (attractors) over multi-dimensional lattices. We describe the thermodynamic formalism of the underlying spin lattice system and then prove existence, uniqueness, mixing properties, and exponential decay of correlations of equilibrium measures for a class of Hölder continuous potential functions with a sufficiently small Hölder constant. We also study finite-dimensional approximations of equilibrium measures in terms of lattice systems (ℤ-approximations) and lattice spin systems (ℤd-approximations). We apply our results to establish existence, uniqueness, and mixing property of SRB-measures as well as obtain the entropy formula.

Original languageEnglish (US)
Pages (from-to)675-711
Number of pages37
JournalCommunications In Mathematical Physics
Volume193
Issue number3
DOIs
StatePublished - Jan 1 1998

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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