On amenable semigroups of rational functions
Dynamical Systems
2021-08-25 v2 Complex Variables
Abstract
We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation. We also prove a number of results about amenable semigroups of arbitrary rational functions. In particular, we show that under quite general conditions a semigroup of rational functions is left amenable if and only if it is a subsemigroup of the centralizer of some rational function.
Cite
@article{arxiv.2008.12194,
title = {On amenable semigroups of rational functions},
author = {Fedor Pakovich},
journal= {arXiv preprint arXiv:2008.12194},
year = {2021}
}
Comments
The extended and polished version