English

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 B\mathcal B), 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