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 language | English |
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Pages (from-to) | 613-626 |
Number of pages | 14 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 477 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2019 Sep 1 |
Keywords
- Cantor sets
- Hausdorff dimension
- Self-similar sets
ASJC Scopus subject areas
- Analysis
- Applied Mathematics