Commuting rational functions revisited

Fedor Pakovich

doi:10.1017/etds.2019.51

Commuting rational functions revisited

Fedor Pakovich

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Pages (from-to)	295-320
Number of pages	26
Journal	Ergodic Theory and Dynamical Systems
Volume	41
Issue number	1
DOIs	https://doi.org/10.1017/etds.2019.51
State	Published - 1 Jan 2021

Keywords

Common iterates
Commuting rational functions
The Ritt theorem

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/etds.2019.51

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Commuting rational functions revisited

Abstract

Keywords

ASJC Scopus subject areas

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