Comptes Rendus
no. 9
Number theory
On the Hausdorff dimension faithfulness of continued fraction expansion
[Sur la fidélité du développement en fraction continue pour la dimension de Hausdorff]

Présenté par : Jean-Pierre Kahane

Jia Liu1 ; Zhenliang Zhang2
1 Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, 233030, Bengbu, PR China
2 School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, 453003, PR China
Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 874-878.

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 n−1 premiers quotients partiels du développement en fraction continue sont fixés et le ne 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.07.009
Jia Liu 1 ; Zhenliang Zhang 2

1 Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, 233030, Bengbu, PR China
2 School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, 453003, PR China 
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Jia Liu; Zhenliang Zhang. On the Hausdorff dimension faithfulness of continued fraction expansion. Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 874-878. doi : 10.1016/j.crma.2016.07.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.07.009/

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