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Entropy of transcendental entire functions

Part of: Complex dynamical systems Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  07 October 2019

ANNA MIRIAM BENINI Open the ORCID record for ANNA MIRIAM BENINI [Opens in a new window] ,
JOHN ERIK FORNÆSS  and
HAN PETERS
ANNA MIRIAM BENINI
Affiliation:
Dipartimento di Scienze Matematiche Fisiche e Informatiche, Università di Parma, Italy email ambenini@gmail.com
JOHN ERIK FORNÆSS
Affiliation:
Department of Mathematical Sciences, NTNU Trondheim, Norway email john.fornass@ntnu.no
HAN PETERS
Affiliation:
Korteweg de Vries Institute for Mathematics, University of Amsterdam, the Netherlands email hanpeters77@gmail.com
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Abstract

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We prove that all transcendental entire functions have infinite topological entropy.

Keywords

transcendental dynamicsentropyhyperbolic metric

MSC classification

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions 30D20: Entire functions, general theory
Secondary: 30D35: Distribution of values, Nevanlinna theory
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 2 , February 2021 , pp. 338 - 348
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Copyright
© Cambridge University Press, 2019

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