# The escaping set for transcendental entire maps

Date:
09.05.12
Times:
16:00 to 17:00
Place:
Universitat Politènica de Catalunya - Aula S05 (FME)
Speaker:
Xavier Jarque
University:
Universitat de Barcelona

Abstract:

We will introduce the escaping set, as an invariant subset of the dynamical plane in holomorphic dynamics. We will briefly discuss the case of polynomials (where the escaping set is just the basin of attraction of infinity) and consider the case of entire transcendental maps where the situation is significantly different. We will present and state some remarkable results of the Eremenko's Conjecture (the connected components of the escaping set are unbounded) and finally we restrict the attention to the complex exponential family to show that for Misiurewicz parameters the escaping set is a connected subset of the complex plane.