Dynamical Systems seminar - Dynamics of Zorich maps

Dates

Wednesday, April 14, 2021 - 13:00 to 14:00

Speaker: Athanasios Tsantaris (University of Nottingham)

Title: Dynamics of Zorich maps

In the theory of one dimensional holomorphic dynamics, one of the most well studied families of maps is the exponential family $E_\lambda(z):=\lambda e^z$. Zorich maps are the quasiregular higher dimensional analogues of the exponential map on the plane. For the exponential family $E_\lambda(z):=\lambda e^z$, $\lambda>0$ it is generally well known that for $0<\lambda\leq 1/e$ the Julia set of $E_\lambda$ is a "Cantor Bouquet" while for $\lambda>1/e$ the Julia set is the entire complex plane. In this talk we will discuss how this dichotomy and many other facts about the exponential family generalize to the higher dimensional setting of Zorich maps.