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Micromeasure distributions and applications for conformally generated fractals

Published online by Cambridge University Press:  12 October 2015

JONATHAN M. FRASER  and
MARK POLLICOTT
JONATHAN M. FRASER
Affiliation:
School of Mathematics, The University of Manchester, Manchester, M13 9PL. e-mail: [email protected]
MARK POLLICOTT
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL. e-mail: [email protected]
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 159 , Issue 3 , November 2015 , pp. 547 - 566
Copyright
Copyright © Cambridge Philosophical Society 2015 

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