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On semiconjugate rational functions

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Abstract

We investigate semiconjugate rational functions, that is rational functions A, B related by the functional equation \({A \circ X = X \circ B}\), where X is a rational function. We show that if A and B is a pair of such functions, then either A can be obtained from B by a certain iterative process, or A and B can be described in terms of orbifolds of non-negative Euler characteristic on the Riemann sphere.

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Authors and Affiliations

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

    Fedor Pakovich

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  1. Fedor Pakovich
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Pakovich, F. On semiconjugate rational functions. Geom. Funct. Anal. 26, 1217–1243 (2016). https://doi.org/10.1007/s00039-016-0383-6

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  • DOI: https://doi.org/10.1007/s00039-016-0383-6

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