Tuen-Wai Ng, HKU, Hong Kong

On finite Blaschke products sharing preimage of connected compact sets 

Abstract

In this talk, we shall consider the problem of characterizing those finite Blaschke products sharing preimage of connected compact subsets with positive hyperbolic capacity of the standard unit disk. We shall see that this problem is closely related to the factorization of finite Blaschke products (in the sense of compositions) and also the problem of characterizing polynomials sharing the same Julia set. To solve this problem, we shall follow T.C. Dinh’s approach to a similar problem for polynomials.This is a joint work with C.Y. Tsang.