Functional equations in polynomials
Dynamical Systems
2020-08-25 v2 Rings and Algebras
Abstract
We determine all F,G in C[X] of degree at least 2 for which the semigroup generated by F and G under composition is not the free semigroup on the letters F and G. We also solve the same problem for F,G in X^2 C[[X]], and prove partial analogues over arbitrary fields.
Cite
@article{arxiv.2008.09554,
title = {Functional equations in polynomials},
author = {Zhan Jiang and Michael E. Zieve},
journal= {arXiv preprint arXiv:2008.09554},
year = {2020}
}