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Transfer operators for coupled analytic maps

By Torsten Fischer and Hans Henrik Rugh

Abstract

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

Topics: QA
Publisher: Cambridge University Press
Year: 2000
OAI identifier: oai:wrap.warwick.ac.uk:824

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