Semigroups of rational functions: some problems and conjectures

TL;DR

This paper explores open problems and conjectures related to semigroups of rational functions under composition, focusing on their properties and connections to amenability in various mathematical contexts.

Contribution

It introduces new problems and conjectures about the structure and properties of semigroups of rational functions, highlighting their relation to amenability.

Findings

Formulation of open problems in semigroups of rational functions

Proposals of conjectures linking these semigroups to amenability

Identification of different contexts where these problems arise

Abstract

We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.