Tadashi Arimitsu, Johannes Jaerisch, Hiroki Sumi, Takayuki Watanabe
Published 2024-03-27Version 1
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.
Related articles:
Bowen's formula for meromorphic functions
Non-autonomous conformal iterated function systems and Moran-set constructions
Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors
![QR code for arXiv:2403.18612 [math.DS]](http://oss.arxitics.com/images/favicon.svg)