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A non-Archimedean Montel’s theorem

Part of: Arithmetic and non-Archimedean dynamical systems Non-Archimedean analysis Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  21 February 2012

Charles Favre ,
Jan Kiwi  and
Eugenio Trucco
Charles Favre
Affiliation:
Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau, Cedex, France (email: favre@math.polytechnique.fr)
Jan Kiwi
Affiliation:
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile (email: jkiwi@puc.cl)
Eugenio Trucco
Affiliation:
Instituto de Ciencias Físicas y Matemáticas, Facultad de Ciencias, Universidad Austral de Chile, Casilla 567, Valdivia, Chile (email: etrucco@uach.cl)
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Abstract

We prove a version of Montel’s theorem for analytic functions over a non-Archimedean complete valued field. We propose a definition of normal family in this context, and give applications of our results to the dynamics of non-Archimedean entire functions.

Keywords

normal family Berkovich spaces non-Archimedean analysis

MSC classification

Secondary: 32P05: Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 37P50: Dynamical systems on Berkovich spaces 30D45: Bloch functions, normal functions, normal families
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 3 , May 2012 , pp. 966 - 990
Copyright
Copyright © Foundation Compositio Mathematica 2012

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