English

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.

Keywords

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

R2 v1 2026-06-23T18:08:42.784Z