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

页码：539 / 568

页数：30

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