2021/02/15 by Hugo Rodrigues Araujo, Araújo, Hugo, Carlos Gustavo Moreira +2
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2102.07283
openalex publication_date 2021/02/15 · openalex created_date 2021/03/01 · openalex updated_date 2026/07/28
In this paper we prove that among pairs K, K' ⊂ ℂ of conformal dynamically defined Cantor sets with sum of Hausdorff dimensions HD(K)+HD(K')>2, there is an open and dense subset of such pairs verifying int(K-K')≠ ∅. This is motivated by the work \citeMY, where Moreira and Yoccoz proved a similar statement for dynamically defined Cantor sets in the real line. Here we adapt their argument to the context of conformal Cantor sets in the complex plane, this requires the introduction of several new concepts and a more detailed analysis in some parts of the argument.