Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts
Dynamical Systems
2011-05-26 v1
Abstract
We prove that for meromorphic maps with logarithmic tracts (e.g. entire or meromorphic maps with a finite number of poles from class ), the Julia set contains a compact invariant hyperbolic Cantor set of Hausdorff dimension greater than 1. Hence, the hyperbolic dimension of the Julia set is greater than 1.
Keywords
Cite
@article{arxiv.0711.2672,
title = {Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts},
author = {Krzysztof Barański and Bogusława Karpińska and Anna Zdunik},
journal= {arXiv preprint arXiv:0711.2672},
year = {2011}
}
Comments
7 pages, 1 figure