Projections of Gibbs measures on self-conformal sets

被引：4

作者：

Bruce, Catherine ^{[1
]}

Jin, Xiong ^{[1
]}

机构：

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

来源：

NONLINEARITY | 2019年 / 32卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Hausdorff dimension; Gibbs measure; self-conformal sets; projections; CP-chain; group extension;

D O I：

10.1088/1361-6544/aaec9f

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that for Gibbs measures on self-conformal sets in R-d (d >= 2) satisfying certain minimal assumptions, without requiring any separation condition, the Hausdorff dimension of orthogonal projections to k-dimensional subspaces is the same and is equal to the maximum possible value in all directions. As a corollary we show that Falconer's distance set conjecture holds for this class of self-conformal sets satisfying the open set condition.

引用

页码：603 / 621

页数：19

共 25 条

[1]

[Anonymous], 2014, FRACTAL GEOMETRY MAT

[2] The scenery flow for hyperbolic Julia sets [J].

Bedford, T ;

Fisher, AM ;

Urbanski, M .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2002, 85 :467-492

[3] Ratio geometry, rigidity and the scenery process for hyperbolic Cantor sets [J].

Bedford, T ;

Fisher, AM .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1997, 17 :531-564

[4]

Bowen R., 1979, PUBL MATH-PARIS, V50, P259, DOI [10.1007/BF02684767, DOI 10.1007/BF02684767]

[5]

BOWEN R., 1975, Lecture Notes in Mathematics, V470

[6]

Falconer K, 2015, FRACTAL GEOMETRY STO, VV, P3

[7] Exact dimensionality and projections of random self-similar measures and sets [J].

Falconer, Kenneth J. ;

Jin, Xiong .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2014, 90 :388-412

[8] Relationships between different dimensions of a measure [J].

Fan, AH ;

Lau, KS ;

Rao, H .

MONATSHEFTE FUR MATHEMATIK, 2002, 135 (03) :191-201

[9] Dimension Theory of Iterated Function Systems [J].

Feng, De-Jun ;

Hu, Huyi .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2009, 62 (11) :1435-1500

[10] Micromeasure distributions and applications for conformally generated fractals [J].

Fraser, Jonathan M. ;

Pollicott, Mark .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2015, 159 (03) :547-566

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