Semiconjugate rational functions: a dynamical approach

F. Pakovich

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arXiv · 1707.02948

Semiconjugate rational functions: a dynamical approach

F. Pakovich

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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.

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BibTeX RIS

F. Pakovich. 2017-07-10. Semiconjugate rational functions: a dynamical approach. https://arxiv.org/abs/1707.02948

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