ON THE HAUSDORFF DIMENSION OF THE RAUZY GASKET

被引：32
|
作者：
Avila, Artur [1 ,2 ]
Hubert, Pascal [3 ]
Skripchenko, Alexandra [4 ]
机构：
[1] Inst Math Jussieu Paris Rive Gauche, CNRS UMR 7586, Batiment Sophie Germain,Case 7021, F-75205 Paris 13, France
[2] IMPA, Estr Dona Castarino 110, BR-22460320 Rio De Janeiro, Brazil
[3] Inst Math Marseille, 39 Rue F Joliot Curie, F-13453 Marseille 20, France
[4] Natl Res Univ Higher Sch Econ, Fac Math, Vavilova St 7, Moscow 112312, Russia
来源：
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE | 2016年 / 144卷 / 03期
关键词：
Systems of isometries; Rauzy induction; Hausdorff dimension; SPACE; TRANSFORMATIONS; PSEUDOGROUPS; THEOREM; TREES;
D O I：
10.24033/bsmf.2722
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove that the Hausdorff dimension of the Rauzy gasket is less than 2. By this result, we answer a question addressed by Pierre Arnoux. Also, this question is a very particular case of the conjecture stated by S.P. Novikov and A. Maltsev in 2003.
引用
收藏
页码：539 / 568
页数：30
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