Comptes Rendus
no. 3
Dynamical Systems
Lipschitz equivalence of self-similar sets
[Equivalence Lipschitz d'ensembles autosimilaires]

Présenté par : Jean-Pierre Kahane

Hui Rao1 ; Huo-Jun Ruan2 ; Li-Feng Xi3
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
Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 191-196.

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)∪(M/5+2/5)∪(M/5+4/5) and M′=(M′/5)∪(M′/5+3/5)∪(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)∪(M/5+2/5)∪(M/5+4/5) et M′=(M′/5)∪(M′/5+3/5)∪(M′/5+4/5). Nous répondons affirmativement à cette question.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.12.016

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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.016/

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