Undecidability of Finite Orbit Recognition in Polynomial Maps

2025/10/01 by Gwon, Gwangyong
#Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2510.00412

Abstract

We prove the undecidability of determining whether a Turing machine yields an eventually periodic trajectory. From this, we deduce the undecidability of orbit finiteness in the polynomial dynamical system on infinite tuples of integers.

Citations

• Upper Bounds on the Sizes of Finite Orbits for Unramified Morphisms
• Did Turing prove the undecidability of the halting problem?
• On periodic orbits of polynomial maps

Related

• On periodic orbits of polynomial maps
• Orbit decidability, applications and variations
• Upper Bounds on the Sizes of Finite Orbits for Unramified Morphisms
• Algebraic Test for Asymptotic Stability of Periodic Orbits for Polynomial Systems
• Orbit Problem Revisited