M4 is regular-closed

Yutaro Himeki; Yutaka Ishii

doi:10.1017/etds.2018.27

M4 is regular-closed

Yutaro Himeki, Yutaka Ishii

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

For each , we investigate a family of iterated function systems which is parameterized by a common contraction ratio <![CDATA[$s\in \mathbb{D}^{\times }\equiv \{s\in \mathbb{C}:0<|s| and possesses a rotational symmetry of order . Let be the locus of contraction ratio for which the corresponding self-similar set is connected. The purpose of this paper is to show that is regular-closed, that is, holds for . This gives a new result for and a simple geometric proof of the previously known result by Bandt and Hung [Fractal -gons and their Mandelbrot sets. NonlinearityA 21 (2008, 2653-2670] for .

Original language	English
Pages (from-to)	213-220
Number of pages	8
Journal	Ergodic Theory and Dynamical Systems
Volume	40
Issue number	1
DOIs	https://doi.org/10.1017/etds.2018.27
Publication status	Published - Jan 1 2020

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1017/etds.2018.27

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M4 is regular-closed

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