The Maximal Entropy Measure of Fatou Boundaries
Dynamical Systems
2017-08-25 v1
Abstract
We look at the maximal entropy (MME) measure of the boundaries of connected components of the Fatou set of a rational map of degree greater than or equal to 2. We show that if there are infinitely many Fatou components, and if either the Julia set is disconnected or the map is hyperbolic, then there can be at most one Fatou component whose boundary has positive MME measure. We also replace hyperbolicity by the more general hypothesis of geometric finiteness.
Keywords
Cite
@article{arxiv.1708.07141,
title = {The Maximal Entropy Measure of Fatou Boundaries},
author = {Jane Hawkins and Michael Taylor},
journal= {arXiv preprint arXiv:1708.07141},
year = {2017}
}