Resumen de Analytic flows on the unit disk: angular derivatives and boundary fixed points

Manuel Domingo Contreras Márquez , Santiago Díaz Madrigal

• We use the concept of angular derivative and the hyperbolic metric in the unit disk D, to study the dynamical aspects of the equilibrium points belonging to ?D of some complex-analytic dynamical systems on D. Our results show a deep connection between the dynamical properties of those equilibrium points and the geometry of certain simply connected domains of C. As a consequence, and in the context of semigroups of analytic functions, we give some geometric insight to a well-known inequality of Cowen and Pommerenke about the angular derivative of an analytic function.