Partial holomorphic semiconjugacies between rational functions

TL;DR

This paper proves the existence of partial holomorphic semiconjugacies between rational functions on the Riemann sphere, defined outside at most one-dimensional sets, advancing understanding of complex dynamics and function conjugacy.

Contribution

It introduces a general framework for partial semiconjugacies between rational functions, extending previous results to broader contexts.

Findings

Existence of partial semiconjugacies on complements of at most one-dimensional sets

Semiconjugacies are holomorphic in a generalized sense

Framework applicable to various rational functions

Abstract

We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are holomorphic in a certain sense.