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arXiv · 2510.00412

Undecidability of Finite Orbit Recognition in Polynomial Maps

Gwangyong Gwon
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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.

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Gwangyong Gwon. 2025-10-01. Undecidability of Finite Orbit Recognition in Polynomial Maps. https://arxiv.org/abs/2510.00412

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