Micromeasure distributions and applications for conformally generated fractals

被引：5

作者：

Fraser, Jonathan M. ^{[1
]}

Pollicott, Mark ^{[2
]}

机构：

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2015年 / 159卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

JULIA SETS; HYPERBOLIC DIMENSION; INVARIANT-MEASURES; DISTANCE SETS; SCENERY FLOW; MAPS; PROJECTIONS; GEOMETRY;

D O I：

10.1017/S0305004115000523

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the scaling scenery of Gibbs measures for subshifts of finite type on self-conformal fractals and applications to Falconer's distance set problem and dimensions of projections. Our analysis includes hyperbolic Julia sets, limit sets of Schottky groups and graph-directed self-similar sets.

引用

页码：547 / 566

页数：20

共 27 条

[1] [Anonymous], P LOND MATH SOC 2
[2] [Anonymous], 2003, Fractal Geometry: Mathematical Foundations and Applications, DOI DOI 10.1002/0470013850
[3] [Anonymous], 1975, LECT NOTES MATH
[4] Avila A, 2008, J AM MATH SOC, V21, P305
[5] Hyperbolic Dimension of Julia Sets of Meromorphic Maps with Logarithmic Tracts
Baranski, Krzysztof
Karpinska, Boguslawa
Zdunik, Anna
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2009, 2009 (04) : 615 - 624
[6] The scenery flow for hyperbolic Julia sets
Bedford, T
Fisher, AM
Urbanski, M
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2002, 85 : 467 - 492
[7] Ratio geometry, rigidity and the scenery process for hyperbolic Cantor sets
Bedford, T
Fisher, AM
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1997, 17 : 531 - 564
[8] On the Erdos-Volkmann and Katz-Tao ring conjectures
Bourgain, J
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2003, 13 (02) : 334 - 365
[9] Erdogan MB, 2005, INT MATH RES NOTICES, V2005, P1411
[10] FALCONER K. J., 2015, FRACTAL GEOMETRY STO

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