An undecidable problem in dynamics

Jason Bell

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arXiv · 2610.22123

An undecidable problem in dynamics

Jason Bell

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Abstract

Given a variety $X$ with a self-map $ϕ$ and subvarieties $Y$ and $Z$ of $X$, we consider the set of $n$ for which $ϕ^n(Y)$ intersects $Z$ nontrivially. Extending a beautiful construction of Lee and Nam, we show this gives rise to an undecidable problem for a fixed ambient variety $X$ and morphism $ϕ$. We further use this construction to give a counterexample to a conjecture of the author, Satriano, and Sierra.

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Jason Bell. 2026-10-15. An undecidable problem in dynamics. https://arxiv.org/abs/2610.22123

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