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Communications in Mathematical Physics

, Volume 193, Issue 3, pp 675–711 | Cite as

Equilibrium Measures for Coupled Map Lattices:¶Existence, Uniqueness and Finite-Dimensional Approximations

  • Miaohua Jiang
  • Yakov B. Pesin

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 (ℤ d -approximations). We apply our results to establish existence, uniqueness, and mixing property of SRB-measures as well as obtain the entropy formula.

Keywords

Entropy Potential Function Exponential Decay Spin System Lattice System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Miaohua Jiang
    • 1
  • Yakov B. Pesin
    • 2
  1. 1.Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332, USAUS
  2. 2.Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USAUS

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