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.
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