Upper Bounds on the Sizes of Finite Orbits for Unramified Morphisms

2025/08/18 by Young Kyun Kim, Kim, Young Kyun · 1 citation
Computer Science · Engineering · #37P55 #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #Optimization and Packing Problems #Optimization and Search Problems

paper · pdf · doi:10.48550/arxiv.2508.12639

openalex publication_date 2025/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for a dynamical system on an algebraic variety over 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.

Citations

• On periodic orbits of polynomial maps
• On Dynamical Cancellation
• Dynamical uniform boundedness and the abc-conjecture
• Current Trends and Open Problems in Arithmetic Dynamics
• Boundedness results for periodic points on algebraic varieties

Cited by

• Undecidability of Finite Orbit Recognition in Polynomial Maps

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