EVENT DETAILS AND ABSTRACT

Title: On semiconjugate rational functions
Speaker: Fedor Pakovich
Speaker Info: Ben Gurion University
Brief Description:
Special Note:
Abstract:

Let A and B be rational functions of degree at least two on the Riemann sphere. The function B is said to be semiconjugate to the function A if there exists a non-constant rational function X such that $A \circ X = X \circ B$. The semiconjugacy relation plays an important role in the classical theory of complex dynamical systems as well as in the new emerging field of arithmetic dynamics. In the talk we present a description of solutions of this semi-conjugacy equation in terms of two-dimensional orbifolds of non-negative Euler characteristic on the Riemann sphere. As an application, we provide an ``effective'' version of the classical theorem Ritt about commuting rational functions.