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arXiv · 1808.05758

Sums of two self-similar Cantor sets

Yuki Takahashi
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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.

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Yuki Takahashi. 2018-08-16. Sums of two self-similar Cantor sets. https://arxiv.org/abs/1808.05758

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