## 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 language | English |
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Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Ergodic Theory and Dynamical Systems |

DOIs | |

Publication status | Accepted/In press - Apr 10 2018 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics