Consider a rational map f on the Riemann sphere of degree at least 2 which has no parabolic periodic points. Assuming that f has Rivera-Letelier's backward contraction property with an arbitrarily large constant, we show that the upper box dimension of the Julia set J(f) is equal to its hyperbolic dimension, by investigating the properties of conformal measures on the Julia set.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-6,
author = {Huaibin Li and Weixiao Shen},
title = {Dimensions of the Julia sets of rational maps with the backward contraction property},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {165-176},
zbl = {1153.37384},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-6}
}
Huaibin Li; Weixiao Shen. Dimensions of the Julia sets of rational maps with the backward contraction property. Fundamenta Mathematicae, Tome 201 (2008) pp. 165-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-2-6/