CENTRAL LIMIT THEOREM FOR DIMENSION OF GIBBS MEASURES IN HYPERBOLIC DYNAMICS

DOI10.1142/S0219493712003675zbMath1247.37029arXiv0912.3170OpenAlexW2038775431WikidataQ126036948 ScholiaQ126036948MaRDI QIDQ5389124

Renaud Leplaideur, Benoît Saussol

Publication date: 24 April 2012

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.3170

zbMATH Keywords

dimensioncentral limit theoremGibbs measureexpanding maps

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20)

Related Items (5)

Multiple Borel-Cantelli lemma in dynamics and multilog law for recurrence ⋮ Central limit theorem for generalized Weierstrass functions ⋮ Quantifying inhomogeneity in fractal sets ⋮ CENTRAL LIMIT THEOREM FOR THE MODULUS OF CONTINUITY OF AVERAGES OF OBSERVABLES ON TRANSVERSAL FAMILIES OF PIECEWISE EXPANDING UNIMODAL MAPS ⋮ Sequential Gibbs measures and factor maps

Cites Work

• Dimension and recurrence in hyperbolic dynamics
• A vector-valued almost sure invariance principle for hyperbolic dynamical systems
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Some relations between dimension and Lyapunov exponents
• Dimension and product structure of hyperbolic measures
• The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
• Recurrence rate in rapidly mixing dynamical systems
• Invariant measures of full dimension for some expanding maps
• The Hausdorff dimension of general Sierpiński carpets
• Thermodynamic Formalism
• Local product structure for Equilibrium States
• A variational principle for the dimension for a class of non-conformal repellers

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