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arXiv · 2011.02163

The entropy of entire transcendental functions

Markus Wendt
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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.

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Markus Wendt. 2020-11-04. The entropy of entire transcendental functions. https://arxiv.org/abs/2011.02163

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