TY - JOUR
T1 - M4 is regular-closed
AU - Himeki, Yutaro
AU - Ishii, Yutaka
N1 - Publisher Copyright:
© Cambridge University Press, 2018.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - For each , we investigate a family of iterated function systems which is parameterized by a common contraction ratio <![CDATA[$s\in \mathbb{D}^{\times }\equiv \{s\in \mathbb{C}:0<|s| and possesses a rotational symmetry of order . Let be the locus of contraction ratio for which the corresponding self-similar set is connected. The purpose of this paper is to show that is regular-closed, that is, holds for . This gives a new result for and a simple geometric proof of the previously known result by Bandt and Hung [Fractal -gons and their Mandelbrot sets. NonlinearityA 21 (2008, 2653-2670] for .
AB - For each , we investigate a family of iterated function systems which is parameterized by a common contraction ratio <![CDATA[$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 .
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U2 - 10.1017/etds.2018.27
DO - 10.1017/etds.2018.27
M3 - Article
AN - SCOPUS:85045133702
SN - 0143-3857
VL - 40
SP - 213
EP - 220
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 1
ER -