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

Hillel Furstenberg

doi:10.3934/jmd.2019027

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

Hillel Furstenberg^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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 ×p-and ×q-Cantor sets.

Original language	English
Pages (from-to)	437-449
Number of pages	13
Journal	Journal of Modern Dynamics
Volume	15
DOIs	https://doi.org/10.3934/jmd.2019027
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019 AIMSCIENCES.

Keywords

Cantor sets
Convolution
Entropy
Hausdorff dimension
L-norm
Partitions
Probability measures
Self-similarity

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10.3934/jmd.2019027

Cite this

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KW - Entropy

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KW - L-norm

KW - Partitions

KW - Probability measures

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

Abstract

Bibliographical note

Keywords

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