The Hausdorff dimension of the escaping set of meromorphic functions (Volker Mayer - Université de Lille)

Séminaire « Analyse complexe et équations différentielles »
Salle de Kampé de Fériet

In the setting of the dynamics of transcendental functions f : \C → \widehat{C}, the escaping set is a dynamically important set and consist in those points whose orbit escape  to infinity.  We present joint work with M. Urbanski in which we obtained a precise formula for the Hausdorff dimension of this set in a very general context. I will survey related results, give applications and present the key ideas of the proof of this result.

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