Dimension properties of the boundaries of exponential basins
Dynamical Systems
2011-05-26 v1
Abstract
We prove that the boundary of a component of the basin of an attracting periodic cycle (of period greater than 1) for an exponential map on the complex plane has Hausdorff dimension greater than 1 and less than 2. Moreover, the set of points in the boundary of which do not escape to infinity has Hausdorff dimension (in fact: hyperbolic dimension) greater than 1, while the set of points in the boundary of which escape to infinity has Hausdorff dimension 1.
Keywords
Cite
@article{arxiv.0902.1065,
title = {Dimension properties of the boundaries of exponential basins},
author = {Krzysztof Barański and Bogusława Karpińska and Anna Zdunik},
journal= {arXiv preprint arXiv:0902.1065},
year = {2011}
}
Comments
13 pages, 1 figure