6 papers · 1 filter
Fatou's associates
Vasiliki Evdoridou, Lasse Rempe, David J. Sixsmith
Suppose that is a transcendental entire function, is a simply connected domain, and is a connected component of . Using Riemann maps, w…
On the connectivity of the escaping set in the punctured plane
Vasiliki Evdoridou, David Martí-Pete, David J. Sixsmith
We consider the dynamics of transcendental self-maps of the punctured plane, . We prove that the escaping set is either connected, or…
Which sequences are orbits?
Daniel A. Nicks, David J. Sixsmith
In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the func…
Dynamics of generalised exponential maps
Patrick Comdühr, Vasiliki Evdoridou, David J. Sixsmith
Since 1984, many authors have studied the dynamics of maps of the form , with . It is now well-known that the Julia set of such a map has an intr…
Spiders' webs in the punctured plane
Vasiliki Evdoridou, David Martí-Pete, David J. Sixsmith
Many authors have studied sets, associated with the dynamics of a transcendental entire function, which have the topological property of being a spider's web. In this paper we adap…
The topology of the set of non-escaping endpoints
Vasiliki Evdoridou, David J. Sixsmith
There are several classes of transcendental entire functions for which the Julia set consists of an uncountable union of disjoint curves each of which joins a finite endpoint to in…