2020/04/09 by Hiromichi Nakayama, Takuya Takahashi, Nakayama, Hiromichi +1
Mathematics · #37E30 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2004.04324
openalex publication_date 2020/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A. Sannami constructed an example of the differentiable Cantor set embedded in the real line whose difference set has a positive measure. In this paper, we generalize the definition of the difference sets for sets of the two dimensional Euclidean space as the sets of vectors between two sets, and estimate their measures. For the quadratic map Qc(z)=z2+c, we obtain that the measure of the difference set of its Julia set vanishes if |c|>3+sqrt3.