Dimensions of orbital sets in complex dynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908605994762240 |
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| author | Fraser, Jonathan M Xu, Yunlong |
| author_facet | Fraser, Jonathan M Xu, Yunlong |
| contents | Let $ E $ be a non-empty compact subset of the Riemann sphere and $T$ be a rational map of degree at least two. We study the associated \emph{orbital set}, that is, the backwards orbit of $E$ under $T$, and study the relationship between the upper box dimension of the orbital set and the upper box dimensions of the Julia set of $T$ and the initial set $ E$. Our results extend previous work on inhomogeneous iterated function systems to the setting of complex dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimensions of orbital sets in complex dynamics Fraser, Jonathan M Xu, Yunlong Dynamical Systems Metric Geometry primary: 37F10, 28A80 secondary: 30C15, 28A78 Let $ E $ be a non-empty compact subset of the Riemann sphere and $T$ be a rational map of degree at least two. We study the associated \emph{orbital set}, that is, the backwards orbit of $E$ under $T$, and study the relationship between the upper box dimension of the orbital set and the upper box dimensions of the Julia set of $T$ and the initial set $ E$. Our results extend previous work on inhomogeneous iterated function systems to the setting of complex dynamical systems. |
| title | Dimensions of orbital sets in complex dynamics |
| topic | Dynamical Systems Metric Geometry primary: 37F10, 28A80 secondary: 30C15, 28A78 |
| url | https://arxiv.org/abs/2510.19456 |