Tuesday, February 14th, 2012
9:30am - 10:30am, in Campus Center 2-2545

Liz Vivas

Purdue University

Dynamics of Holomorphic Self-maps near a Fixed Point

Abstract: The local dynamics of holomorphic self-maps of C^n around a fixed point has been an object of study since the time of Schroeder, Fatou and Julia. In this talk we will explain the results known for n = 1 and the partial known results for n > 1. We will focus in the case n = 2 and of maps tangents to the identity, that is, when the derivative of our self-map at the fixed point is the Identity. In this case the usual tools of linearization introduced by Poincare are not possible to use and some new techniques are required.