Sums of two self-similar Cantor sets

2018/08/16 by Takahashi, Yuki · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.05758

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.

Cited by

• The algebraic difference of a Cantor set and its complement

Related

• Sums of two homogeneous Cantor sets
• The interior of randomly perturbed self-similar sets on the line
• Resonance between Cantor sets
• Self-similar subsets of the Cantor set
• Open intervals in sums and products of Cantor sets