Gibbs properties of self-conformal measures and the multifractal formalism

被引：34
|
作者：
Feng, De-Jun [1 ]
机构：
[1] Chinese Univ Hong Kong, Dept Math, Sha Tin, Hong Kong, Peoples R China
[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2007年 / 27卷
关键词：
D O I：
10.1017/S0143385706000952
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that for any self-conformal measures, without any separation conditions, the multifractal formalism partially holds. The result follows by establishing certain Gibbs properties for self-conformal measures.
引用
收藏
页码：787 / 812
页数：26
相关论文
共 50 条
  • [1] Self-conformal multifractal measures
    Patzschke, N
    [J]. ADVANCES IN APPLIED MATHEMATICS, 1997, 19 (04) : 486 - 513
  • [2] Multifractal of self-conformal measures
    Ye, YL
    [J]. NONLINEARITY, 2005, 18 (05) : 2111 - 2133
  • [3] MIXED SELF-CONFORMAL MULTIFRACTAL MEASURES
    Meifeng Dai Nonlinear Scientific Research Center Faculty of Science Jiangsu University Jiangsu
    [J]. Analysis in Theory and Applications, 2009, 25 (02) : 154 - 165
  • [4] Projections of Gibbs measures on self-conformal sets
    Bruce, Catherine
    Jin, Xiong
    [J]. NONLINEARITY, 2019, 32 (02) : 603 - 621
  • [5] The average density of self-conformal measures
    Zähle, M
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2001, 63 : 721 - 734
  • [6] Diophantine approximation and self-conformal measures
    Urbanski, M
    [J]. JOURNAL OF NUMBER THEORY, 2005, 110 (02) : 219 - 235
  • [7] Divergence points of self-conformal measures
    Wang, Pei
    Ji, Yong
    Chen, Ercai
    Zhang, Yaqing
    [J]. MONATSHEFTE FUR MATHEMATIK, 2019, 189 (04): : 735 - 763
  • [8] Divergence points of self-conformal measures
    Pei Wang
    Yong Ji
    Ercai Chen
    Yaqing Zhang
    [J]. Monatshefte für Mathematik, 2019, 189 : 735 - 763
  • [9] Multifractal formalism for the inverse of random weak Gibbs measures
    Yuan, Zhihui
    [J]. STOCHASTICS AND DYNAMICS, 2020, 20 (04)
  • [10] Results on the dimension spectrum for self-conformal measures
    Rams, Michal
    Vehel, Jacques Levy
    [J]. NONLINEARITY, 2007, 20 (04) : 965 - 973
12345