Commuting rational functions revisited

Abstract

Let $B$ be a rational function of degree at least two that is neither a Lattès map nor conjugate to $z^{\pm n}$ or $\pm T_n$. We provide a method for describing the set $C_B$ consisting of all rational functions commuting with $B.$ Specifically, we define an equivalence relation $\underset{B}{\sim }$ on $C_B$ such that the quotient $C_B/\underset{B}{\sim }$ possesses the structure of a finite group $G_B$, and describe generators of $G_B$ in terms of the fundamental group of a special graph associated with $B$.

The final version

References in corpus (1)

• Finiteness theorems for commuting and semiconjugate rational functions

Cited by in corpus (2)

• Lower bounds for genera of fiber products
• On algebraic dependencies between Poincaré functions