Micromeasure distributions and applications for conformally generated fractals
arXiv:1502.05609 · doi:10.1017/S0305004115000523
Abstract
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.
17 pages, 1 figure