Dimensions of the Julia sets of rational maps with the backward contraction property

Huaibin Li, and Weixiao Shen. "Dimensions of the Julia sets of rational maps with the backward contraction property." Fundamenta Mathematicae 198.2 (2008): 165-176. <http://eudml.org/doc/283081>.

@article{HuaibinLi2008,
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.},
author = {Huaibin Li, Weixiao Shen},
journal = {Fundamenta Mathematicae},
keywords = {Julia set; conformal measure; rational map; hyperbolic dimension; box dimension; backward contracting map},
language = {eng},
number = {2},
pages = {165-176},
title = {Dimensions of the Julia sets of rational maps with the backward contraction property},
url = {http://eudml.org/doc/283081},
volume = {198},
year = {2008},
}

TY - JOUR
AU - Huaibin Li
AU - Weixiao Shen
TI - Dimensions of the Julia sets of rational maps with the backward contraction property
JO - Fundamenta Mathematicae
PY - 2008
VL - 198
IS - 2
SP - 165
EP - 176
AB - 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.
LA - eng
KW - Julia set; conformal measure; rational map; hyperbolic dimension; box dimension; backward contracting map
UR - http://eudml.org/doc/283081
ER -