Sums of two self-similar Cantor sets

Yuki Takahashi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We show that for any pair of self-similar Cantor sets with sum of Hausdorff dimensions greater than 1, one can create an interval in the sumset by applying arbitrary small perturbations (without leaving the class of self-similar Cantor sets). In our setting the perturbations have more freedom than in the setting of the Palis' conjecture, so our result can be viewed as an affirmative answer to a weaker form of the Palis' conjecture.

Original languageEnglish
Pages (from-to)613-626
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume477
Issue number1
DOIs
Publication statusPublished - 2019 Sep 1

Keywords

  • Cantor sets
  • Hausdorff dimension
  • Self-similar sets

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Sums of two self-similar Cantor sets'. Together they form a unique fingerprint.

Cite this