Ergodic properties of Viana-like maps with singularities in the base dynamics

DOI10.1090/S0002-9939-2013-11680-1zbMath1297.37013arXiv1109.0849OpenAlexW1979999801MaRDI QIDQ2846922

Daniel Schnellmann, José F. Alves

Publication date: 4 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.0849

zbMATH Keywords

central limit theoremlarge deviationslocal limit theoremdecay of correlationsBerry-Esseen theoremViana mapsalmost sure invariance principle

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Dynamical aspects of measure-preserving transformations (37A05) Ergodicity, mixing, rates of mixing (37A25) Large deviations (60F10) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (8)

Analytic skew-products of quadratic polynomials over Misiurewicz-Thurston maps ⋮ (Semi)continuity of the entropy of Sinai probability measures for partially hyperbolic diffeomorphisms ⋮ Large Deviations of the Ergodic Averages: From Hölder Continuity to Continuity Almost Everywhere ⋮ Viana maps driven by Benedicks-Carleson quadratic maps ⋮ Statistical properties of generalized Viana maps ⋮ Absolutely continuous invariant measures for random non-uniformly expanding maps ⋮ A Borel-Cantelli lemma and its applications ⋮ Young towers for product systems

Cites Work

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• Positive Lyapunov exponents for quadratic skew-products over a Misiurewicz–Thurston map
• Weakly expanding skew-products of quadratic maps
• Statistical stability for robust classes of maps with non-uniform expansion
• Strong statistical stability of non-uniformly expanding maps
• Non-continuous weakly expanding skew-products of quadratic maps with two positive Lyapunov exponents

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