Undecidability of Finite Orbit Recognition in Polynomial Maps
Logic
2026-05-19 v3 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2510.00412,
title = {Undecidability of Finite Orbit Recognition in Polynomial Maps},
author = {Gwangyong Gwon},
journal= {arXiv preprint arXiv:2510.00412},
year = {2026}
}