On semiconjugate rational functions

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We investigate semiconjugate rational functions, that is rational functions A, B related by the functional equation A∘ X= X∘ 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.

Original languageEnglish
Pages (from-to)1217-1243
Number of pages27
JournalGeometric and Functional Analysis
Issue number4
StatePublished - 1 Jul 2016


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