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arXiv · 1502.05609

Micromeasure distributions and applications for conformally generated fractals

Jonathan M. Fraser·Mark Pollicott
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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.

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Jonathan M. Fraser, Mark Pollicott. 2015-02-19. Micromeasure distributions and applications for conformally generated fractals. https://doi.org/10.1017/s0305004115000523

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