On Hausdorff dimension of invariant sets for expanding maps of a circle

DOI10.1017/S0143385700003461zbMath0631.58019MaRDI QIDQ3768050

Mariusz Urbański

Publication date: 1986

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

pressureinvariant measurestopological entropyLebesgue measureexpanding mapDE-perturbationsHausdorff dimension of invariant setsLyapunov exponent of ergodic measure

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical systems involving maps of the circle (37E10) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Topological entropy (37B40) Dynamical systems with hyperbolic behavior (37D99)

Related Items (17)

Density spectrum of Cantor measure ⋮ On numbers badly approximable by dyadic rationals ⋮ Horseshoes for diffeomorphisms preserving hyperbolic measures ⋮ Entropy continuity for interval maps with holes ⋮ Essential dynamics for Lorenz maps on the real line and the lexicographical world ⋮ The bifurcation locus for numbers of bounded type ⋮ Two bifurcation sets arising from the beta transformation with a hole at 0 ⋮ Critical values for the -transformation with a hole at ⋮ The shrinking target problem for matrix transformations of tori: revisiting the standard problem ⋮ Exceptional sets for nonuniformly hyperbolic diffeomorphisms ⋮ Intermediate \(\beta\)-shifts as greedy \(\beta\)-shifts with a hole ⋮ The local Hölder exponent for the dimension of invariant subsets of the circle ⋮ The -transformation with a hole at 0 ⋮ On the Existence of Conformal Measures ⋮ The local Hölder exponent for the entropy of real unimodal maps ⋮ Complexity and fractal dimensions for infinite sequences with positive entropy ⋮ The bifurcation set as a topological invariant for one-dimensional dynamics

Cites Work

• Unnamed Item
• Hausdorff dimension of quasi-circles
• Symbolic Dynamics and Transformations of the Unit Interval
• Endomorphisms of Compact Differentiable Manifolds
• Differentiable dynamical systems
• Periodic Points and Measures for Axiom a Diffeomorphisms

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