Commuting rational functions revisited

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3 Scopus citations

Abstract

Let B be a rational function of degree at least two that is neither a Lattès map nor conjugate to z±n or ±Tn. We provide a method for describing the set Cb consisting of all rational functions commuting with B. Specifically, we define an equivalence relation ∼B on Cb such that the quotient Cb/∼B possesses the structure of a finite group Cb, and describe generators of in terms of Cb the fundamental group of a special graph associated with B.

Original languageEnglish
Pages (from-to)295-320
Number of pages26
JournalErgodic Theory and Dynamical Systems
Volume41
Issue number1
DOIs
StatePublished - 1 Jan 2021

Keywords

  • Common iterates
  • Commuting rational functions
  • The Ritt theorem

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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