{\mathcal{M}}:{4} is regular-closed

YUTARO HIMEKI, Yutaka Ishii

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1 Citation (Scopus)

Abstract

For each (Formula presented.), we investigate a family of iterated function systems which is parameterized by a common contraction ratio (Formula presented.) and possesses a rotational symmetry of order (Formula presented.). Let (Formula presented.) be the locus of contraction ratio (Formula presented.) for which the corresponding self-similar set is connected. The purpose of this paper is to show that (Formula presented.) is regular-closed, that is, (Formula presented.) holds for (Formula presented.). This gives a new result for (Formula presented.) and a simple geometric proof of the previously known result by Bandt and Hung [Fractal (Formula presented.)-gons and their Mandelbrot sets. Nonlinearity 21 (2008), 2653–2670] for (Formula presented.).

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalErgodic Theory and Dynamical Systems
DOIs
Publication statusAccepted/In press - Apr 10 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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