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


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.


Entropy Potential Function Exponential Decay Spin System Lattice System 
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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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