Multifractal analysis of homological growth rates for hyperbolic surfaces

被引：0
|
作者：
Jaerisch, Johannes [1 ]
Takahasi, Hiroki [2 ]
机构：
[1] Nagoya Univ, Grad Sch Math, Chikusaku, Nagoya 4648602, Japan
[2] Keio Univ, Keio Inst Pure & Appl Sci KiPAS, Dept Math, Yokohama 2238522, Japan
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2024年
关键词：
Fuchsian group; Bowen-Series map; thermodynamic formalism; multifractal analysis; CONFORMAL EXPANDING MAPS; WEAK GIBBS MEASURES; EQUILIBRIUM MEASURES; THERMODYNAMIC FORMALISM; LYAPUNOV SPECTRUM; POINTS; INTERVALS; SYSTEMS;
D O I：
10.1017/etds.2024.62
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level sets of prescribed growth rates in terms of a generalized Poincar & eacute; exponent of the Fuchsian group. We employ symbolic dynamics developed by Bowen and Series, ergodic theory and thermodynamic formalism to prove the analyticity of the dimension spectrum.
引用
收藏
页数：35
相关论文
共 50 条
  • [1] A multifractal analysis for cuspidal windings on hyperbolic surfaces
    Jaerisch, Johannes
    Kesseboehmer, Marc
    Munday, Sara
    [J]. STOCHASTICS AND DYNAMICS, 2021, 21 (03)
  • [2] Multifractal analysis of hyperbolic flows
    Barreira, L
    Saussol, B
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 214 (02) : 339 - 371
  • [3] Multifractal Analysis of Hyperbolic Flows
    L. Barreira
    B. Saussol
    [J]. Communications in Mathematical Physics, 2000, 214 : 339 - 371
  • [4] Multifractal analysis of growing surfaces
    Chaudhari, A
    Yan, CCS
    Lee, SL
    [J]. APPLIED SURFACE SCIENCE, 2004, 238 (1-4) : 513 - 517
  • [5] The rates of growth in a hyperbolic group
    Fujiwara, Koji
    Sela, Zlil
    [J]. INVENTIONES MATHEMATICAE, 2023, 233 (03) : 1427 - 1470
  • [6] The rates of growth in a hyperbolic group
    Koji Fujiwara
    Zlil Sela
    [J]. Inventiones mathematicae, 2023, 233 : 1427 - 1470
  • [7] A homological characterization of hyperbolic groups
    D. J. Allcock
    S. M. Gersten
    [J]. Inventiones mathematicae, 1999, 135 : 723 - 742
  • [8] A homological characterization of hyperbolic groups
    Allcock, DJ
    Gersten, SM
    [J]. INVENTIONES MATHEMATICAE, 1999, 135 (03) : 723 - 742
  • [9] Multifractal and Stochastic analysis of electropolished surfaces
    Haase, M
    Mora, A
    Lehle, B
    [J]. THINKING IN PATTERNS: FRACTALS AND RELATED PHENOMENA IN NATURE, 2004, : 69 - 78
  • [10] Multifractal analysis of textured silicon surfaces
    Jurecka, Stanislav
    Angermann, Heike
    Kobayashi, Hikaru
    Takahashi, Masao
    Pincik, Emil
    [J]. APPLIED SURFACE SCIENCE, 2014, 301 : 46 - 50
12345