Hausdorff and packing measure functions of self-similar sets: continuity and measurability

DOI10.1017/S0143385707000922zbMath1168.37007OpenAlexW2158827108MaRDI QIDQ3623590

L. Olsen

Publication date: 21 April 2009

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

Full work available at URL: https://doi.org/10.1017/s0143385707000922

zbMATH Keywords

self-similar fractalsHausdorff measure and dimension

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78) Dimension theory of smooth dynamical systems (37C45)

Related Items (5)

Packing measure of super separated iterated function systems ⋮ Continuity of the Hausdorff measure of continued fractions and countable alphabet iterated function systems ⋮ Continuity of packing measure functions of self-similar iterated function systems ⋮ Regularity of Hausdorff measure function for conformal dynamical systems ⋮ A note on Hausdorff measures of self-similar sets in R^d

Cites Work

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• Measures and self similarity
• Self-similarity
• Hausdorff dimension and conformal dynamics. II: Geometrically finite rational maps
• A multifractal formalism
• The Hausdorff measure of a Sierpinski carpet
• Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase
• Packing Measure, and its Evaluation for a Brownian Path
• On the structure of self-similar fractals
• Exact Hausdorff measure and intervals of maximum density for Cantor sets
• Continuity of Attractors and Invariant Measures for Iterated Function Systems

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