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
相关论文
共 50 条
  • [1] LOWER BOUNDS ON THE DIMENSION OF THE RAUZY GASKET
    Gutierrez-Romo, Rodolfo
    Matheus, Carlos
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2020, 148 (02): : 321 - 327
  • [2] AN UPPER BOUND ON THE DIMENSION OF THE RAUZY GASKET
    Pollicott, Mark
    Sewell, Benedict
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2023, 151 (04): : 595 - 611
  • [3] THE HAUSDORFF DIMENSION OF THE CLE GASKET
    Miller, Jason
    Sun, Nike
    Wilson, David B.
    ANNALS OF PROBABILITY, 2014, 42 (04): : 1644 - 1665
  • [4] Hausdorff dimension of the Apollonian gasket
    Vytnova, Polina L.
    Wormell, Caroline L.
    INVENTIONES MATHEMATICAE, 2025, 239 (03) : 909 - 946
  • [5] PRECISE CALCULATION OF HAUSDORFF DIMENSION OF APOLLONIAN GASKET
    Bai, Zai-Qiao
    Finch, Steven R.
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2018, 26 (04)
  • [6] On Hausdorff dimension monotonicity of a family of dynamical subsets of Rauzy fractals
    Nowak, W. Georg
    Scheicher, Klaus
    Sirvent, Victor F.
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2015, 11 (04) : 1089 - 1098
  • [7] On the Hausdorff dimension of the Sierpinski gasket with respect to the harmonic metric
    Teufl, E
    FRACTALS IN GRAZ 2001: ANALYSIS - DYNAMICS - GEOMETRY - STOCHASTICS, 2003, : 263 - 269
  • [8] An elementary proof that the Rauzy gasket is fractal
    Pollicott, Mark
    Sewell, Benedict
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2024, 44 (07) : 1913 - 1922
  • [9] Hausdorff measure of Sierpinski gasket
    周作领
    Science China Mathematics, 1997, (10) : 1016 - 1021
  • [10] Hausdorff measure of Sierpinski gasket
    Zuoling Zhou
    Science in China Series A: Mathematics, 1997, 40 : 1016 - 1021
12345