Analytic flows in the unit disk: angular derivatives and boundary fixed points

We use the concept of angular derivative and the hyperbolic metric in the unit diskD, to study the dynamical aspects of the equilibrium points belong-ing to ∂D of some complex-analytic dynamical systems on D. Our results show a deep connection between the dynamical properties of those equilib-rium 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. 1