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On semiconjugate rational functions

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Fedor Pakovich
Ben Gurion University of the Negev/MPI
Tue, 2017-09-12 14:00 - 15:00
MPIM Lecture Hall

Let A and B be rational functions 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 condition generalises both the classical conjugacy relation and
the commutativity condition. In the talk we present a description of solutions of
functional equaton (*) in terms of orbifolds of non-negative Euler characteristic on
the Riemann sphere, and discuss numerous relations of this equation with complex
dynamics and number theory.

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