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- W1479883398 abstract "This chapter discusses the theory of Gibbs measures for Anosov and Axiom A diffeomorphism. It gives the classical theory of Gibbs measures for one-dimensional lattices in statistical mechanics. Based on this, the modern theory of Gibbs measures for Anosov and Axiom A maps are developed. The chapter describes many properties of Gibbs measures–statistical, topological, and others (some of them very recent). It focuses on one special Gibbs measure—the so-called Sinai–Ruelle–Bowen (SRB) measure. The theory of Gibbs measures is presented in the chapter in detail and with complete proofs. The chapter discusses Anosov and Axiom A flows and their Gibbs measures, including SRB measures. It also discusses recent results on the decay of correlations. The chapter presents a discussion on nonuniformly hyperbolic diffeomorphism and recent studies of the leakage of mass near Axiom A basic sets and Anosov diffeomorphism with holes, including the escape-rate formula and conditionally invariant measures." @default.
- W1479883398 created "2016-06-24" @default.
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- W1479883398 date "2002-01-01" @default.
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- W1479883398 title "Chapter 4 Invariant measures for hyperbolic dynamical systems" @default.
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- W1479883398 doi "https://doi.org/10.1016/s1874-575x(02)80006-6" @default.
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