On amenable semigroups of rational functions
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 arXiv:
 arXiv:2008.12194
 Bibcode:
 2020arXiv200812194P
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Complex Variables
 EPrint:
 The extended and polished version