Strict Hölder Equivalence of Self-Similar Sets
Abstract
The study of Lipschitz equivalence of fractals is a very active topic in recent years. It is natural to ask when two fractal sets are strictly Hölder equivalent. In the present paper, we completely characterize the strict Hölder equivalence for two classes of self-similar sets: the first class is totally disconnected fractal cubes and the second class is self-similar sets with two branches which satisfy the strong separation condition.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Computability
Logic
AI Algorithms
semigroups and automata theory
Publication details
- Journal / source
- Wuhan University Journal of Natural Sciences
- Publisher
- EDP Sciences
- Volume
- 31
- Issue
- 4
- Pages
- 325–328
- Publication date
- 1 August 2026
- Language
- EN