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arXiv · 2510.19456

Dimensions of orbital sets in complex dynamics

Jonathan M Fraser·Yunlong Xu
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Abstract

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.

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Jonathan M Fraser, Yunlong Xu. 2025-10-22. Dimensions of orbital sets in complex dynamics. https://arxiv.org/abs/2510.19456

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