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arXiv · 1609.04271

Lipschitz equivalence of fractals and finite state automaton

Hui Rao·Yunjie Zhu
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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.

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Hui Rao, Yunjie Zhu. 2016-09-14. Lipschitz equivalence of fractals and finite state automaton. https://arxiv.org/abs/1609.04271

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