Dimensions of the Julia sets of rational maps with the backward contraction property
Volume 198 / 2008
Fundamenta Mathematicae 198 (2008), 165-176
MSC: Primary 37F35.
DOI: 10.4064/fm198-2-6
Abstract
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.
