Non-archimedean connected Julia sets with branching
Dynamical Systems
2015-04-08 v2 Number Theory
Abstract
We construct the first examples of rational functions defined over a non-archimedean field with certain dynamical properties. In particular, we find such functions whose Julia sets, in the Berkovich projective line, are 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 show for some of our examples that the measure-theoretic entropy is strictly smaller than the topological entropy, thus answering a question of Favre and Rivera-Letelier.
Keywords
Cite
@article{arxiv.1410.0591,
title = {Non-archimedean connected Julia sets with branching},
author = {Dvij Bajpai and Robert L. Benedetto and Ruqian Chen and Edward Kim and Owen Marschall and Darius Onul and Yang Xiao},
journal= {arXiv preprint arXiv:1410.0591},
year = {2015}
}
Comments
Minor revisions, including simplified computation of Gurevich entropy