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

Hillel Furstenberg

doi:10.3934/jmd.2019027

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2019, Volume 15: 437-449. Doi: 10.3934/jmd.2019027 open access

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From invariance to self-similarity: The work of Michael Hochman on fractal dimension and its aftermath (Brin Prize article)

Hillel Furstenberg

Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Received: November 20, 2019

Published: December 2019

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Abstract

M. Hochman's work on the dimension of self-similar sets has given impetus to resolving other questions regarding fractal dimension. We describe Hochman's approach and its influence on the subsequent resolution by P. Shmerkin of the conjecture on the dimension of the intersection of $ \times p $- and $ \times q $-Cantor sets.

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Mathematics Subject Classification: Primary: 28A80, 37C45; Secondary: 11K55, 11B30.

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References

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