Lipschitz equivalence of fractals and finite state automaton

Abstract

The study of Lipschitz equivalence of fractals is a very active topic in recent years. Most of the studies in literature concern totally disconnected fractals. In this paper, using finite state automata, we construct a bi-Lipschitz map between two fractal squares which are not totally disconnected. This is the first non-trivial map of this type. We also show that this map is measure-preserving.

18 pages, 7 figures

References in corpus (3)

• Lipschitz equivalence of self-similar sets and hyperbolic boundaries
• Lipschitz Equivalence Class, Ideal Class and the Gauss Class Number Problem
• Lipschitz invariance of walk dimension on connected self-similar sets

Cited by in corpus (1)

• Elementary fractal geometry. 4. Automata-generated topological spaces