Work

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

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2403.18612

Authors: Arimitsu, Tadashi, Jaerisch, Johannes, Sumi, Hiroki, Watanabe, Takayuki

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4393300470

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