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Quasi-Lipschitz equivalence of fractals

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Abstract

The paper proves that if E and F are dust-like C 1 self-conformal sets with \(0 < \mathcal{H}^{\dim _H E} (E),\mathcal{H}^{\dim _H F} (F) < \infty \), then there exists a bijection f: E å F such that

$$\frac{{(dim_H F)log|f(x) - f(y)|}}{{(dim_H E)log|x - y|}} \to 1$$

uniformly as |x−y} å 0. It is also proved that a self-similar arc is Hölder equivalent to [0, 1] if and only if it is a quasi-arc.

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Authors and Affiliations

  1. Institute of Mathematics, Zhejiang Wanli University, 315100, Ningbo, Zhejiang, P. R. China

    Li-Feng Xi

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  1. Li-Feng Xi
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Additional information

Research supported by National Natural Science Foundation of China (No. 10241003, 10301029) and Morningside Center of Mathematics in Beijing.

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Xi, LF. Quasi-Lipschitz equivalence of fractals. Isr. J. Math. 160, 1–21 (2007). https://doi.org/10.1007/s11856-007-0053-3

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  • DOI: https://doi.org/10.1007/s11856-007-0053-3

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