Lipschitz equivalence of self-similar sets with two-state neighbor automaton
| Autor: | Yunjie Zhu, Ya-min Yang |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Finite-state machine Applied Mathematics 010102 general mathematics State (functional analysis) Lipschitz continuity 01 natural sciences 010305 fluids & plasmas Lipschitz domain Totally disconnected space Hausdorff dimension 0103 physical sciences 0101 mathematics Equivalence (measure theory) Analysis Separation property Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 458:379-392 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2017.09.007 |
| Popis: | The study of Lipschitz equivalence of fractals is a very active topic in recent years, but there are very few results on fractals which is not totally disconnected. In this paper, using finite state automata and the angle separation property, we prove that for a class of self-similar sets with two-state neighbor automaton, two elements are Lipschitz equivalent if and only if they have the same Hausdorff dimension. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect