38 research outputs found
Transfer operators for coupled analytic maps
We consider analytically coupled circle maps (uniformly expanding and analytic) on the -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 âcluster expansionâ-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