# Eventually stable rational functions

```@article{Jones2016EventuallySR,
title={Eventually stable rational functions},
author={Rafe Jones and Alon Y. Levy},
journal={arXiv: Number Theory},
year={2016}
}```
• Published 2 March 2016
• Mathematics
• arXiv: Number Theory
For a field K, rational function phi in K(z) of degree at least two, and alpha in P^1(K), we study the polynomials in K[z] whose roots are given by the solutions to phi^n(z) = alpha, where phi^n denotes the nth iterate of phi. When the number of irreducible factors of these polynomials stabilizes as n grows, the pair (phi, alpha) is called eventually stable over K. We conjecture that (phi, alpha) is eventually stable over K when K is any global field and alpha any point not periodic under phi…
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