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Semiconjugate Rational Functions: A Dynamical Approach

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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 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.

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Acknowledgements

The author is grateful to A. Eremenko for discussions.

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Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, 8410501, Beer Sheba, Israel

    F. Pakovich

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  1. F. Pakovich
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Pakovich, F. Semiconjugate Rational Functions: A Dynamical Approach. Arnold Math J. 4, 59–68 (2018). https://doi.org/10.1007/s40598-018-0081-6

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  • DOI: https://doi.org/10.1007/s40598-018-0081-6

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