TOPOLOGY AUTOMATON AND HÖLDER EQUIVALENCE OF BARAŃSKI CARPETS

Yunjie Zhu (), Liang-Yi Huang and Chunbo Cheng ()
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Yunjie Zhu: Department of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435000, P. R. China
Liang-Yi Huang: College of Science, Wuhan University of Science and Technology, Wuhan 430070, P. R. China
Chunbo Cheng: Department of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435000, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 05, 1-16

Abstract: The study of Lipschitz equivalence of fractals is a very active topic in recent years. In 2023, Huang et al. [Topology automaton of self-similar sets and its applications to metrical classifications, Nonlinearity 36 (2023) 2541–2566] studied the Hölder and Lipschitz equivalence of a class of p.c.f. self-similar sets which are not totally disconnected. The main tool they used is the so-called topology automaton. In this paper, we define topology automaton for Barański carpets, and we show that the method used in Huang et al. still works for the self-affine and non-p.c.f. settings. As an application, we obtain a very general sufficient condition for Barański carpets to be Hölder (or Lipschitz) equivalent.

Keywords: Topology Automaton; Barański Capet; Hölder Equivalence (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500495

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