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

• Autores: Manuel Domingo Contreras Márquez, Santiago Díaz Madrigal
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 222, Nº 2, 2005, págs. 253-286
• Idioma: inglés
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• Resumen

  • 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.