Year: 2008
Type: article
Abstract: We prove that for meromorphic maps with logarithmic tracts (in particular, for transcendental maps in the class , which are entire or meromorphic with a finite number of poles), 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.
DOI: 10.1093/imrn/rnn141
Authors: K. Baranski, B. Karpinska, A. Zdunik
Institutions: University of Warsaw, Warsaw University of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Ministerstwo Edukacji i Nauki
OpenAlex ID: W1995444576