The entropy of entire transcendental functions
Dynamical Systems
2020-11-05 v1
Abstract
We use Bowen's definition of topological entropy and Ahlfors five islands theorem, as well as the theory of polynomial-like mappings, to show that the topological entropy of any entire transcendental function is infinity. In addition the entropy is concentrated on the Julia set for each meromorphic function which has no wandering domains.
Keywords
Cite
@article{arxiv.2011.02163,
title = {The entropy of entire transcendental functions},
author = {Markus Wendt},
journal= {arXiv preprint arXiv:2011.02163},
year = {2020}
}