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Uniform perfectness of the attractor of bi-Lipschitz IFS

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Abstract

In this paper, we prove that the attractor of C 1,α bi-Lipschitz IFS in ℝ is uniformly perfect if it is not a singleton. Then we construct an example to show that this does not hold for C 1 bi-Lipschitz IFS in ℝn.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Ruan Huojun, Sun Yeshun & Yin Yongcheng

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  1. Ruan Huojun
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  2. Sun Yeshun
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  3. Yin Yongcheng
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Correspondence to Ruan Huojun.

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Ruan, H., Sun, Y. & Yin, Y. Uniform perfectness of the attractor of bi-Lipschitz IFS. SCI CHINA SER A 49, 433–438 (2006). https://doi.org/10.1007/s11425-006-0433-x

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  • DOI: https://doi.org/10.1007/s11425-006-0433-x

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