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Arnold Mathematical Journal

, Volume 4, Issue 1, pp 59–68 | Cite as

Semiconjugate Rational Functions: A Dynamical Approach

  • F. Pakovich
Research Contribution
  • 47 Downloads

Abstract

Using dynamical methods we give a new proof of the theorem saying that if ABX are rational functions of complex variable z 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.

Keywords

Semiconjugate rational functions Poincaré functions Invariant curves Galois closure Orbifolds 

Notes

Acknowledgements

The author is grateful to A. Eremenko for discussions.

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Copyright information

© Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2018

Authors and Affiliations

  1. 1.Department of MathematicsBen Gurion University of the NegevBeer ShebaIsrael

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