Lipschitz equivalence of self-similar sets

Hui Rao; Huo-Jun Ruan; Li-Feng Xi

doi:10.1016/j.crma.2005.12.016

Dynamical Systems

Lipschitz equivalence of self-similar sets

Presented by: Jean-Pierre Kahane

Hui Rao ¹; Huo-Jun Ruan ²; Li-Feng Xi ³

¹Department of Mathematics, Tsinghua University, Beijing, 100084, China
²Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
³Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, China

Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 191-196

Abstract (Original language)
Résumé

In 1997 David and Semmes asked whether there exists a bilipschitz map between the two compact self-similar subset M and $M^{'}$ of the real line defined by the relations $M = (M / 5) \cup (M / 5 + 2 / 5) \cup (M / 5 + 4 / 5)$ and $M^{'} = (M^{'} / 5) \cup (M^{'} / 5 + 3 / 5) \cup (M^{'} / 5 + 4 / 5)$ . We answer this question positively.

En 1997, David et Semmes ont posé la question de savoir s'il existe une application bi-lipschitzienne entre les deux compacts linéaires M et $M^{'}$ définis par les relations $M = (M / 5) \cup (M / 5 + 2 / 5) \cup (M / 5 + 4 / 5)$ et $M^{'} = (M^{'} / 5) \cup (M^{'} / 5 + 3 / 5) \cup (M^{'} / 5 + 4 / 5)$ . Nous répondons affirmativement à cette question.

Received: 2005-11-23
Accepted: 2005-12-07
Published online: 2006-01-05

DOI: 10.1016/j.crma.2005.12.016

Author's affiliations:

Hui Rao ¹ ; Huo-Jun Ruan ² ; Li-Feng Xi ³

¹ Department of Mathematics, Tsinghua University, Beijing, 100084, China
² Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
³ Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, China

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Hui Rao; Huo-Jun Ruan; Li-Feng Xi. Lipschitz equivalence of self-similar sets. Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 191-196. doi: 10.1016/j.crma.2005.12.016

References
Cited by

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