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Non-archimedean connected Julia sets with branching

Published online by Cambridge University Press:  12 October 2015

DVIJ BAJPAI ,
ROBERT L. BENEDETTO ,
RUQIAN CHEN ,
EDWARD KIM ,
OWEN MARSCHALL ,
DARIUS ONUL  and
YANG XIAO
DVIJ BAJPAI
Affiliation:
Amherst College, Amherst, MA 01002, USA email dbajpai15@amherst.edu, rlbenedetto@amherst.edu, ejkim15@amherst.edu, omarschall15@amherst.edu, donul15@amherst.edu
ROBERT L. BENEDETTO
Affiliation:
Amherst College, Amherst, MA 01002, USA email dbajpai15@amherst.edu, rlbenedetto@amherst.edu, ejkim15@amherst.edu, omarschall15@amherst.edu, donul15@amherst.edu
RUQIAN CHEN
Affiliation:
University of Illinois, Urbana, IL 68101, USA email rchen40@illinois.edu
EDWARD KIM
Affiliation:
Amherst College, Amherst, MA 01002, USA email dbajpai15@amherst.edu, rlbenedetto@amherst.edu, ejkim15@amherst.edu, omarschall15@amherst.edu, donul15@amherst.edu
OWEN MARSCHALL
Affiliation:
Amherst College, Amherst, MA 01002, USA email dbajpai15@amherst.edu, rlbenedetto@amherst.edu, ejkim15@amherst.edu, omarschall15@amherst.edu, donul15@amherst.edu
DARIUS ONUL
Affiliation:
Amherst College, Amherst, MA 01002, USA email dbajpai15@amherst.edu, rlbenedetto@amherst.edu, ejkim15@amherst.edu, omarschall15@amherst.edu, donul15@amherst.edu
YANG XIAO
Affiliation:
Brown University, Providence, RI 02912, USA email ynxysunny@gmail.com
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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
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 1 , February 2017 , pp. 59 - 78
Copyright
© Cambridge University Press, 2015 

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