On semiconjugate rational functions

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 ca...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 26; no. 4; pp. 1217 - 1243
Main Author Pakovich, Fedor
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2016
Springer Nature B.V
Subjects
Analysis
Functional equations
Mathematics
Mathematics and Statistics
Rational functions
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-016-0383-6