A non-archimedean Montel's theorem

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.

29 pages, minor modifications, to appear in Compositio

References in corpus (2)

• On Limits of Sequences of Holomorphic Functions
• Topology and Geometry of the Berkovich Ramification Locus for Rational Functions

Cited by in corpus (5)

• Dynamics on Berkovich spaces in low dimensions
• Lehto--Virtanen-type and big Picard-type theorems for Berkovich analytic spaces
• Oscillating Wandering Domains for p-Adic Transcendental Entire Maps
• Julia sets and geometrically finite maps over finite extensions of the $p$-adic field
• Activity measures of dynamical systems over non-archimedean fields