On semiconjugate rational functions

• Published in: Geometric and functional analysis Vol. 26; no. 4; pp. 1217 - 1243
• Main Author: Pakovich, Fedor
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.07.2016; Springer Nature B.V
• Subjects: Analysis; Functional equations; Mathematics; Mathematics and Statistics; 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...