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• W3003205919 abstract "For a class of piecewise hyperbolic maps in two dimensions, we propose a combinatorial definition of topological entropy by counting the maximal, open, connected components of the phase space on which iterates of the map are smooth. We prove that this quantity dominates the measure theoretic entropies of all invariant probability measures of the system, and then construct an invariant measure whose entropy equals the proposed topological entropy. We prove that our measure is the unique measure of maximal entropy, that it is ergodic, gives positive measure to every open set, and has exponential decay of correlations against Holder continuous functions. As a consequence, we also prove a lower bound on the rate of growth of periodic orbits. The main tool used in the paper is the construction of anisotropic Banach spaces of distributions on which the relevant weighted transfer operator has a spectral gap. We then construct our measure of maximal entropy by taking a product of left and right maximal eigenvectors of this operator." @default.
• W3003205919 created "2020-02-07" @default.
• W3003205919 creator A5012740429 @default.
• W3003205919 date "2020-01-27" @default.
• W3003205919 modified "2023-09-27" @default.
• W3003205919 title "Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps" @default.
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• W3003205919 hasPublicationYear "2020" @default.
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