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
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
收藏
页码:547 / 566
页数:20
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