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Lipschitz equivalence of fractals and finite state automaton

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.

preprint2016arXivOpen access
Hui RaoYunjie Zhu
math.DS
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Open access2 authors1 topic
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Hui RaoYunjie Zhu

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