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arXiv · 2403.18612

Bowen's formula for a rational graph-directed Markov system

Tadashi Arimitsu·Johannes Jaerisch·Hiroki Sumi·Takayuki Watanabe
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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.

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Tadashi Arimitsu, Johannes Jaerisch, Hiroki Sumi, Takayuki Watanabe. 2024-03-27. Bowen's formula for a rational graph-directed Markov system. https://arxiv.org/abs/2403.18612

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