English

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}
}