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Sliding possibility of the Julia sets
Sliding possibility of the Julia sets
- Publication Year :
- 2020
-
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}.<br />Comment: 7 pages, 2 figures
- Subjects :
- Mathematics - Dynamical Systems
37E30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2004.04324
- Document Type :
- Working Paper