Student Dynamics/Geometry Topology Seminar

Given a nonconstant holomorphic map on the Riemann sphere, we can look at the forward images of any given point under iteration by this map. The grand orbit of a point z under this map is the set of all points whose orbits eventually will intersect the orbit of z. In this talk, we will look at when the grand orbit of a point is finite. In particular, we will look at the grand orbit finite set (also known as the exceptional set) of a given map, which consists of all points with finite grand orbit. We will outline some of the key properties of the grand orbit finite set of a map and use these properties to provide a classification of grand orbit finite sets, showing why points in this set are called "exceptional". We will conclude by outlining some properties of the Julia set that come from understanding the grand orbit finite set.
Speaker(s): Schinella D'Souza (University of Michigan)