2024/12/01 by Yunjie Zhu, Zhu, Yunjie, Huang, Liang-yi +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2412.00694
openalex publication_date 2024/12/01 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28
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.