Connecting ergodicity and dimension in dynamical systems

DOI10.1017/S014338570000568XzbMath0691.58023OpenAlexW1996734275MaRDI QIDQ3033020

Colleen D. Cutler

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1017/s014338570000568x

zbMATH Keywords

dynamical systemsHausdorff measurepointwise dimensionergodic distributionsdimensional distribution

Mathematics Subject Classification ID

Ergodic theory (37A99)

Related Items (20)

On the multifractal analysis of a non-standard branching random walk ⋮ Some remarks on absolute continuity and quantization of probability measures ⋮ Hausdorff and packing spectra, large deviations, and free energy for branching random walks in \({\mathbb{R}^d}\) ⋮ On the exact dimension of Mandelbrot measure ⋮ Local dimension for piecewise monotonic maps on the interval ⋮ Strong and weak duality principles for fractal dimension in Euclidean space ⋮ Hausdorff and packing dimensions of Mandelbrot measure ⋮ On the multifractal analysis of branching random walk on Galton-Watson tree with random metric ⋮ The spectrum of Poincaré recurrence ⋮ Some results on the behavior and estimation of the fractal dimensions of distributions on attractors ⋮ Dimension, recurrence via entropy and Lyapunov exponents for map with singularities ⋮ An intermediate-value theorem for the upper quantization dimension ⋮ On the dimension of deterministic and random Cantor-like sets, symbolic dynamics, and the Eckmann-Ruelle conjecture ⋮ Multifractal Tubes ⋮ The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples ⋮ The Besicovitch weak-packing property ⋮ Multifractal analysis of a measure of multifractal exact dimension ⋮ On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions ⋮ A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions ⋮ \(L^p(\mu)\)-estimation of tangent maps

Cites Work

• Unnamed Item
• A note on equivalent interval covering systems for Hausdorff dimension on \(\mathbb R\)
• Estimation of dimension for spatially distributed data and related limit theorems
• Dimension estimates for attractors
• The Hausdorff Dimension Distribution of Finite Measures in Euclidean Space
• Ergodic theory of chaos and strange attractors

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