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arXiv · 2508.12639

Upper Bounds on the Sizes of Finite Orbits for Unramified Morphisms

Young Kyun Kim
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Abstract

We prove that for a dynamical system on an algebraic variety over $\overline{\mathbb{Q}}$ generated by finitely many unramified endomorphisms, it is decidable whether a given point has a finite orbit. This is achieved by establishing an effective upper bound for the size of finite orbits in integral algebraic dynamical systems with unramified morphisms.

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Young Kyun Kim. 2025-08-18. Upper Bounds on the Sizes of Finite Orbits for Unramified Morphisms. https://arxiv.org/abs/2508.12639

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