Semiconjugate rational functions: a dynamical approach

Abstract

Using dynamical methods we give a new proof of the theorem saying that if $A,B,X$ are rational functions of degree at least two such that $A\circ X=X\circ B$ and $\mathbb{C}(B,X)=\mathbb{C}(z)$, then the Galois closure of the field extension $\mathbb{C}(z)/\mathbb{C}(X)$ has genus zero or one.

An extended version

References in corpus (2)

• Finiteness theorems for commuting and semiconjugate rational functions
• On generalized Lattès maps