Bowen's formula for a rational graph-directed Markov system
Dynamical Systems
2024-03-28 v1
Abstract
We establish Bowen's formula for the Julia set of a non-elementary, expanding, irreducible and aperiodic rational graph-directed Markov system satisfying the backward separating condition. Towards this end, we shall prove that the associated skew product map is topologically exact on the skew product Julia set, and satisfies the density of repelling periodic points. Moreover, we give a criterion for expandingness in terms of hyperbolicity.
Keywords
Cite
@article{arxiv.2403.18612,
title = {Bowen's formula for a rational graph-directed Markov system},
author = {Tadashi Arimitsu and Johannes Jaerisch and Hiroki Sumi and Takayuki Watanabe},
journal= {arXiv preprint arXiv:2403.18612},
year = {2024}
}