TOPOLOGY AUTOMATON AND HÖLDER EQUIVALENCE OF BARAŃSKI CARPETS
YUNJIE ZHU, Liangyi Huang, CHUNBO CHENG · Fractals · 2025
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.