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Non-archimedean connected Julia sets with branching

Published online by Cambridge University Press:  12 October 2015

DVIJ BAJPAI
Affiliation:
ROBERT L. BENEDETTO
Affiliation:
RUQIAN CHEN
Affiliation:
University of Illinois, Urbana, IL 68101, USA email [email protected]
EDWARD KIM
Affiliation:
OWEN MARSCHALL
Affiliation:
DARIUS ONUL
Affiliation:
YANG XIAO
Affiliation:
Brown University, Providence, RI 02912, USA email [email protected]

Abstract

We construct the first examples of rational functions defined over a non-archimedean field with a certain dynamical property: the Julia set in the Berkovich projective line is connected but not contained in a line segment. We also show how to compute the measure-theoretic and topological entropy of such maps. In particular, we give an example for which the measure-theoretic entropy is strictly smaller than the topological entropy, thus answering a question of Favre and Rivera-Letelier.

Type
Research Article
Copyright
© Cambridge University Press, 2015 

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