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arXiv · 2504.04088

Strict Hölder equivalence of self-similar sets

Yanfang Zhang·Xinhui Liu
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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.

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Yanfang Zhang, Xinhui Liu. 2025-04-05. Strict Hölder equivalence of self-similar sets. https://arxiv.org/abs/2504.04088

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