Some relations between Hausdorff-dimensions and entropies

DOI10.1007/BF02871841zbMath0918.58039OpenAlexW1970734376MaRDI QIDQ1286700

Xiongping Dai, Xiangyi Geng, Zuo Ling Zhou

Publication date: 19 August 1999

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02871841

zbMATH Keywords

invariant measuresHausdorff dimensionlocal entropyexpansive homeomorphism

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Ergodic theory (37A99)

Related Items (12)

Unnamed Item ⋮ Logarithmic expansion, entropy, and dimension for set-valued maps ⋮ On various entropies of set-valued maps ⋮ On the continuity of the topological entropy of non-autonomous dynamical systems ⋮ Topological and measure-theoretical entropies of nonautonomous dynamical systems ⋮ Topological entropy of free semigroup actions for noncompact sets ⋮ Fractal metrics of Ruelle expanding maps and expanding ratios ⋮ Pesin topological entropy of nonautonomous dynamical systems ⋮ ON HAUSDORFF DIMENSION AND TOPOLOGICAL ENTROPY ⋮ Constant slope, entropy, and horseshoes for a map on a tame graph ⋮ Entropy inequalities for semigroup actions ⋮ An entropy formula over the dynamical balls and its applications

Cites Work

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• Equivalent conditions for hyperbolic coordinates
• Some relations between dimension and Lyapunov exponents
• Expansive canonical coordinates are hyperbolic
• Expansiveness, hyperbolicity and Hausdorff dimension
• The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
• Dimension, entropy and Lyapunov exponents
• Finitely presented dynamical systems
• Entropy for Group Endomorphisms and Homogeneous Spaces

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