Expanding repellers in limit sets for iterations of holomorphic functions

@article{FeliksPrzytycki2005,
abstract = {We prove that for Ω being an immediate basin of attraction to an attracting fixed point for a rational mapping of the Riemann sphere, and for an ergodic invariant measure μ on the boundary FrΩ, with positive Lyapunov exponent, there is an invariant subset of FrΩ which is an expanding repeller of Hausdorff dimension arbitrarily close to the Hausdorff dimension of μ. We also prove generalizations and a geometric coding tree abstract version. The paper is a continuation of a paper in Fund. Math. 145 (1994) by the author and Anna Zdunik, where the density of periodic orbits in FrΩ was proved.},
author = {Feliks Przytycki},
journal = {Fundamenta Mathematicae},
keywords = {boundary of basin of attraction; iteration of rational map; Hausdorff dimension; hyperbolic dimension; coding tree; Pesin theory; Katok theory},
language = {eng},
number = {1},
pages = {85-96},
title = {Expanding repellers in limit sets for iterations of holomorphic functions},
url = {http://eudml.org/doc/283124},
volume = {186},
year = {2005},
}

TY - JOUR
AU - Feliks Przytycki
TI - Expanding repellers in limit sets for iterations of holomorphic functions
JO - Fundamenta Mathematicae
PY - 2005
VL - 186
IS - 1
SP - 85
EP - 96
AB - We prove that for Ω being an immediate basin of attraction to an attracting fixed point for a rational mapping of the Riemann sphere, and for an ergodic invariant measure μ on the boundary FrΩ, with positive Lyapunov exponent, there is an invariant subset of FrΩ which is an expanding repeller of Hausdorff dimension arbitrarily close to the Hausdorff dimension of μ. We also prove generalizations and a geometric coding tree abstract version. The paper is a continuation of a paper in Fund. Math. 145 (1994) by the author and Anna Zdunik, where the density of periodic orbits in FrΩ was proved.
LA - eng
KW - boundary of basin of attraction; iteration of rational map; Hausdorff dimension; hyperbolic dimension; coding tree; Pesin theory; Katok theory
UR - http://eudml.org/doc/283124
ER -