Jiang, Miaohua; Pesin, Yakov B. Equilibrium measures for coupled map lattices: Existence, uniqueness and finite-dimensional approximations. (English) Zbl 0944.37005 Commun. Math. Phys. 193, No. 3, 675-711 (1998). 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. Reviewer: Alexander Kachurovskij (Novosibirsk) Cited in 1 ReviewCited in 26 Documents MSC: 37A60 Dynamical aspects of statistical mechanics 37K60 Lattice dynamics; integrable lattice equations Keywords:Sinai-Bowen-Ruelle measures; thermodynamical formalism; finite-dimensional approximation PDFBibTeX XMLCite \textit{M. Jiang} and \textit{Y. B. Pesin}, Commun. Math. Phys. 193, No. 3, 675--711 (1998; Zbl 0944.37005) Full Text: DOI