Invariant subsets of expanding mappings of the circle

DOI10.1017/S0143385700004247zbMath0653.58031MaRDI QIDQ3799383

Mariusz Urbański

Publication date: 1987

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

zbMATH Keywords

entropyHausdorff dimensiontopological pressureexpanding map

Mathematics Subject Classification ID

Dynamical systems with hyperbolic behavior (37D99)

Related Items (21)

Horseshoes for diffeomorphisms preserving hyperbolic measures ⋮ Unnamed Item ⋮ Dimension of self-affine sets with holes ⋮ On the Perron-Frobenius-ruelle operator for rational maps on the riemann sphere and for Hölder continuous functions ⋮ Two bifurcation sets arising from the beta transformation with a hole at 0 ⋮ Critical values for the -transformation with a hole at ⋮ Structure and dimension of invariant subsets of expanding Markov maps and joint invariance ⋮ Topological and ergodic properties of symmetric sub-shifts ⋮ The waiting spectra of the sets described by the quantitative waiting time indicators ⋮ The -transformation with a hole at 0 ⋮ Matching for generalised \(\beta\)-transformations ⋮ On the Existence of Conformal Measures ⋮ Large deviations and the distribution of pre-images of rational maps ⋮ Possible jumps of entropy for interval maps ⋮ Continuity of the Hausdorff dimension for piecewise monotonic maps ⋮ Stability of the topological pressure for piecewise monotonic maps under \(C^1\)-perturbations ⋮ The probability distribution and Hausdorff dimension of self-affine functions ⋮ On the specification property and synchronization of uniqueq-expansions ⋮ The bifurcation set as a topological invariant for one-dimensional dynamics ⋮ Exceptional sets in homogeneous spaces and Hausdorff dimension ⋮ Porcupine-Like Horseshoes: Topological and Ergodic Aspects

Cites Work

• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy
• Hausdorff dimension of quasi-circles
• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. II
• The structure of Lorenz attractors
• Ergodic properties of invariant measures for piecewise monotonic transformations
• Theory of dynamical systems and general transformation groups with invariant measure
• Some systems with unique equilibrium states
• On the entropy of a flow

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