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

Hillel Furstenberg

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)437-449
Number of pages13
JournalJournal of Modern Dynamics
Volume15
DOIs
StatePublished - 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 AIMSCIENCES.

Keywords

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

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