From invariance to self-similarity: the work of Michael Hochman on fractal dimension and its aftermath

DOI10.3934/jmd.2019027zbMath1467.28008OpenAlexW2998611355MaRDI QIDQ2026748

Hillel Furstenberg

Publication date: 20 May 2021

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jmd.2019027

zbMATH Keywords

partitionsentropyconvolutionself-similarityHausdorff dimensionCantor setsprobability measures\(L^q\)-norm

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Dimension theory of smooth dynamical systems (37C45) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

• On self-similar sets with overlaps and inverse theorems for entropy
• On Furstenberg's intersection conjecture, self-similar measures, and the \(L^q\) norms of convolutions
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Unnamed Item

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