Fischer, Torsten; Rugh, Hans Henrik Transfer operators for coupled analytic maps. (English) Zbl 0984.37025 Ergodic Theory Dyn. Syst. 20, No. 1, 109-143 (2000). Summary: We consider analytically coupled circle maps (uniformly expanding and analytic) on the \(\mathbb{Z}^d\)-lattice with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures whose finite-dimensional marginals have analytic, exponentially bounded densities. Using residue calculus and ‘cluster expansion’-like techniques we define transfer operators on these Banach spaces. We get a unique (in the considered Banach spaces) probability measure that exhibits exponential decay of correlations. Cited in 7 Documents MSC: 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems 37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 37A25 Ergodicity, mixing, rates of mixing Keywords:exponentially decaying interaction; exponential decay of correlations PDFBibTeX XMLCite \textit{T. Fischer} and \textit{H. H. Rugh}, Ergodic Theory Dyn. Syst. 20, No. 1, 109--143 (2000; Zbl 0984.37025) Full Text: DOI arXiv