Nous montrons dans cette Note que la famille de toutes les unions finies de cylindres consécutifs de même rang n (une telle union est la clôture de l'ensemble des nombres réels dans l'intervalle unité dont les premiers quotients partiels du développement en fraction continue sont fixés et le est astreint à parcourir un ensemble donné d'entiers consécutifs) est fidèle pour la dimension de Hausdorff de l'intervalle unité.
In this note, we show that the family of all possible unions of finite consecutive cylinders of the same rank of continued fraction expansion is faithful for the Hausdorff dimension calculation on the unit interval.
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@article{CRMATH_2016__354_9_874_0, author = {Liu, Jia and Zhang, Zhenliang}, title = {On the {Hausdorff} dimension faithfulness of continued fraction expansion}, journal = {Comptes Rendus. Math\'ematique}, pages = {874--878}, publisher = {Elsevier}, volume = {354}, number = {9}, year = {2016}, doi = {10.1016/j.crma.2016.07.009}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2016.07.009/} }
TY - JOUR AU - Liu, Jia AU - Zhang, Zhenliang TI - On the Hausdorff dimension faithfulness of continued fraction expansion JO - Comptes Rendus. Mathématique PY - 2016 SP - 874 EP - 878 VL - 354 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.07.009/ DO - 10.1016/j.crma.2016.07.009 LA - en ID - CRMATH_2016__354_9_874_0 ER -
%0 Journal Article %A Liu, Jia %A Zhang, Zhenliang %T On the Hausdorff dimension faithfulness of continued fraction expansion %J Comptes Rendus. Mathématique %D 2016 %P 874-878 %V 354 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.07.009/ %R 10.1016/j.crma.2016.07.009 %G en %F CRMATH_2016__354_9_874_0
Liu, Jia; Zhang, Zhenliang. On the Hausdorff dimension faithfulness of continued fraction expansion. Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 874-878. doi : 10.1016/j.crma.2016.07.009. http://www.numdam.org/articles/10.1016/j.crma.2016.07.009/
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