|Location:||MSRI: Online/Virtual, Simons Auditorium|
To participate in this seminar, please register HERE.
When studying the dynamics of an entire map, its escaping set, consisting of all points that converge to infinity under iteration, is of particular importance. With infinity being an essential singularity in the transcendental case, a rich variety of phenomena arise. A key role is played by the subset of points that escape at a ''maximum speed'', known as the fast escaping set.
In this series of two talks, we will introduce these sets and discuss their role in transcendental dynamics. We will focus on their main properties and how they relate to the Julia and Fatou set in the first talk, while we will discuss the existence of spiders' webs and the connection of these sets to the problem of commuting functions in the second.
The (Fast) Escaping Set of a Transcendental Entire Function Pt I