Semiconjugate Rational Functions: A Dynamical Approach

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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

Original languageEnglish
Pages (from-to)59-68
Number of pages10
JournalArnold Mathematical Journal
Volume4
Issue number1
DOIs
StatePublished - 1 Apr 2018

Keywords

  • Galois closure
  • Invariant curves
  • Orbifolds
  • Poincaré functions
  • Semiconjugate rational functions

ASJC Scopus subject areas

  • General Mathematics

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