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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2403.18612 |
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| _version_ | 1866914730450354176 |
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| author | Arimitsu, Tadashi Jaerisch, Johannes Sumi, Hiroki Watanabe, Takayuki |
| author_facet | Arimitsu, Tadashi Jaerisch, Johannes Sumi, Hiroki Watanabe, Takayuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bowen's formula for a rational graph-directed Markov system Arimitsu, Tadashi Jaerisch, Johannes Sumi, Hiroki Watanabe, Takayuki Dynamical Systems 37F10, 58F23, 30D05, 37H12 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. |
| title | Bowen's formula for a rational graph-directed Markov system |
| topic | Dynamical Systems 37F10, 58F23, 30D05, 37H12 |
| url | https://arxiv.org/abs/2403.18612 |