Convergence of moments for Axiom A and non-uniformly hyperbolic flows (Q2908172)

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scientific article; zbMATH DE number 6076566
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Convergence of moments for Axiom A and non-uniformly hyperbolic flows
scientific article; zbMATH DE number 6076566

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    Convergence of moments for Axiom A and non-uniformly hyperbolic flows (English)
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    4 September 2012
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    convergence of moments
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    uniformly hyperbolic
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    non-uniformly hyperbolic
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    Young towers
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    Hénon-like attractor
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    Lorenz attractors
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    The authors prove convergence of moments of all orders for Axiom A diffeomorphisms and flows (the proof is different from [\textit{C. T. McMullen}, Invent. Math. 173, No. 2, 365--425 (2008; Zbl 1156.30035)]). The same results hold for non-uniformly hyperbolic diffeomorphisms and flows modeled by Young towers with superpolynomial tails. For polynomial tails, the authors prove convergence of moments up to a certain order, and give examples where moments diverge when this order is exceeded. Non-uniformly hyperbolic systems covered by their result include Hénon-like attractors, Lorenz attractors, semidispersing billiards, finite horizon planar periodic Lorentz gases, and Pomeau-Manneville intermittency maps.
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