Bounded Geometry in the Supports of Ergodic Invariant Probability Measures

DOI10.1142/S0218127498001625zbMath0948.37021OpenAlexW2042389353MaRDI QIDQ4941355

Jun Hu

Publication date: 30 July 2000

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127498001625

zbMATH Keywords

Hausdorff dimensionLebesgue measureboundary of chaosCantor set of bounded geometryergodic \(f\)-invariant probability measurefinitely many turning pointsnew smooth regularityperiodic orbit of \(f\)

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dimension theory of smooth dynamical systems (37C45)

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Cites Work

• Julia-Fatou-Sullivan theory for real one-dimensional dynamics
• Measure and dimension of solenoidal attractors of one-dimensional dynamical systems
• Topological conjugacy of circle diffeomorphisms