LIPSCHITZ EQUIVALENCE OF SELF-SIMILAR SETS AND FINITE-STATE AUTOMATON

Yunjie Zhu () and Hui Rao
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Yunjie Zhu: School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, P. R. China
Hui Rao: Department of Mathematics and Statistics, Hua Zhong Normal University, Wuhan, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-9

Abstract: The study of Lipschitz equivalence of fractals is a very active topic in recent years. Most of the studies in literature concern totally disconnected fractals. In this paper, using neighbor automata of self-similar sets and a transducer, we construct a bi-Lipschitz map between two fractal squares which are not totally disconnected. This is the first nontrivial construction of this type. We also show that this map is measure-preserving.

Keywords: Self-Similar Set; Lipschitz Equivalence; Finite-State Automaton (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21502716

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