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

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 Holder continuous potential functions with a suf-ciently small Holder constant. We also study nite-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