Sums of two self-similar Cantor sets

Yuki Takahashi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number1
Publication statusPublished - 2019 Sep 1


  • Cantor sets
  • Hausdorff dimension
  • Self-similar sets

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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