On semi-conjugate rational functions

Speaker
Fedor Pakovich, Ben-Gurion University
Date
06/05/2018 - 13:00 - 12:00Add to Calendar 2018-05-06 12:00:00 2018-05-06 13:00:00 On semi-conjugate rational functions Let $A$ and $B$ be rational functions on the Riemann sphere. The function $B$ is said to be semi-conjugate to the function $A$  if there exists a non-constant rational function $X$ such that $$ A\circ X=X\circ B.  (*) $$ The semi-conjugacy condition generalises both the classical conjugacy relation and the commutativity condition. In the talk we present a description of solutions of functional equation (*) 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. Mathematics Colloquium Room 201, Building 216 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Mathematics Colloquium Room 201, Building 216
Abstract

Let $A$ and $B$ be rational functions on the Riemann sphere. The function $B$ is said to be semi-conjugate to the function $A$  if
there exists a non-constant rational function $X$ such that
$$
A\circ X=X\circ B.  (*)
$$
The semi-conjugacy condition generalises both the classical conjugacy relation and the commutativity condition. In the talk we present a description of solutions of functional equation (*) 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.

תאריך עדכון אחרון : 30/04/2018