Sliding possibility of the Julia sets

Hiromichi Nakayama; Takuya Takahashi

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arXiv · 2004.04324

Sliding possibility of the Julia sets

Hiromichi Nakayama·Takuya Takahashi

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Abstract

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 Q_c(z)=z^2+c, we obtain that the measure of the difference set of its Julia set vanishes if |c|>3+sqrt{3}.

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Hiromichi Nakayama, Takuya Takahashi. 2020-04-09. Sliding possibility of the Julia sets. https://arxiv.org/abs/2004.04324

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