On semiconjugate rational functions - Pakovich, Fedor (Geometric and functional analysis, 2016)
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.