The entropy of entire transcendental functions

Published 4 Nov 2020 in math.DS | (2011.02163v1)

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

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