Xavier Jarque (Universitat de Barcelona): The escaping set for transcendental entire maps

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.