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Equilibrium measures for coupled map lattices: Existence, uniqueness and finite-dimensional approximations. (English) Zbl 0944.37005
Authors’ 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 ($$\mathbb{Z}$$-approximations) and lattice spin systems ($$\mathbb{Z}^d$$-approximations). We apply our results to establish existence, uniqueness, and mixing property of SRB-measures as well as obtain the entropy formula.

##### MSC:
 37A60 Dynamical aspects of statistical mechanics 37K60 Lattice dynamics; integrable lattice equations
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