# Dr. Vasiliki Evdoridou (Universidad de Barcelona): "Non escaping endpoints of entire functions"

Dec 15, 2016 from 10:15 AM to 11:59 PM

LMS 4 - Raum 312

Let f_a= e^z+a, a<-1. The Julia set of f_a consists of an uncountable

union of disjoint curves going off to infinity (a Cantor bouquet).

Following several interesting results on the endpoints of these curves,

we consider the set of non-escaping endpoints, that is, the endpoints

whose iterates do not tend to infinity. We show that the union of

non-escaping endpoints with infinity is a totally separated set by

finding continua that separate these endpoints from infinity. This is a

complementary result to the very recent result of Alhabib and

Rempre-Gillen that for the same family of functions the set of escaping

endpoints together with infinity is connected. Moreover, we present

other functions in the exponential family as well as a function that was

first studied by Fatou which share the same property of the non-escaping

endpoints. Finally, we show how we can use the continua we have

constructed in order to show that the union of the Fatou set with the

set of points that escape to infinity 'as quickly as possible' has the

structure of a 'spider's web'.

Auf Einladung von Herrn Prof. Bergweiler.