Spiders' webs in the punctured plane [ Back ]

Date:
18.03.19   
Times:
09:00 to 10:00
Place:
IMUB-Universitat de Barcelona
Speaker:
David Martí-Pete
University:
IMPAN

Abstract

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 adapt the definition of a spider's web to the punctured plane. We give several characterisations of this topological structure, and study the connection with the usual spider's web in the complex plane. We show that there are many transcendental self-maps of $\mathbb C^*$ for which the Julia set is such a spider's web, and we construct the first example of a transcendental self-map of $\mathbb C^*$ for which the escaping set is such a spider's web. This is a joint work with Vasso Evdoridou and Dave Sixsmith.