In 1997 David and Semmes asked whether there exists a bilipschitz map between the two compact self-similar subset M and of the real line defined by the relations and . 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 définis par les relations et . Nous répondons affirmativement à cette question.
Accepted:
Published online:
@article{CRMATH_2006__342_3_191_0, author = {Rao, Hui and Ruan, Huo-Jun and Xi, Li-Feng}, title = {Lipschitz equivalence of self-similar sets}, journal = {Comptes Rendus. Math\'ematique}, pages = {191--196}, publisher = {Elsevier}, volume = {342}, number = {3}, year = {2006}, doi = {10.1016/j.crma.2005.12.016}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.12.016/} }
TY - JOUR AU - Rao, Hui AU - Ruan, Huo-Jun AU - Xi, Li-Feng TI - Lipschitz equivalence of self-similar sets JO - Comptes Rendus. Mathématique PY - 2006 SP - 191 EP - 196 VL - 342 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.12.016/ DO - 10.1016/j.crma.2005.12.016 LA - en ID - CRMATH_2006__342_3_191_0 ER -
%0 Journal Article %A Rao, Hui %A Ruan, Huo-Jun %A Xi, Li-Feng %T Lipschitz equivalence of self-similar sets %J Comptes Rendus. Mathématique %D 2006 %P 191-196 %V 342 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.12.016/ %R 10.1016/j.crma.2005.12.016 %G en %F CRMATH_2006__342_3_191_0
Rao, Hui; Ruan, Huo-Jun; Xi, Li-Feng. 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. http://archive.numdam.org/articles/10.1016/j.crma.2005.12.016/
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