An exceptional set in the ergodic theory of expanding maps on manifolds

DOI10.1007/s00605-005-0391-3zbMath1120.37012OpenAlexW1973093970MaRDI QIDQ996076

J. Martínez

Publication date: 11 September 2007

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-005-0391-3

zbMATH Keywords

dimension theoryasymptotic distribution phenomenonBillingley dimensionBirkhoff's pointwise ergodic theorem

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Fractals (28A80) Exterior differential systems (Cartan theory) (58A15) Hausdorff and packing measures (28A78) Dimension theory of smooth dynamical systems (37C45)

Related Items (7)

Dimension estimates for sets of uniformly badly approximable systems of linear forms ⋮ Jarník-type inequalities ⋮ Simultaneous dense and nondense orbits for commuting maps ⋮ Dimension estimates for the set of points with non-dense orbit in homogeneous spaces ⋮ Effective uniqueness of Parry measure and exceptional sets in ergodic theory ⋮ The topological entropy of non-dense orbits and generalized Schmidt games ⋮ Simultaneously non-dense orbits under different expanding maps

Cites Work

• Unnamed Item
• An exceptional set in the ergodic theory of rational maps of the Riemann sphere
• An Exceptional Set in the Ergodic Theory of Markov Maps of the Interval
• The Hausdorff dimension of the set of points with nondense orbit under a hyperbolic dynamical system
• Sets of Fractional Dimensions which Occur in Some Problems of Number Theory

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