GT ADG-Systèmes Dynamiques

Thermodynamic formalism for entire functions and integral means spectrum of logarithmic tracts
Volker Mayer (Lille 1)
Tuesday 21 November 2017 14:00 -  Orléans -  Salle de Séminaire

Résumé :
We present joint work with M. Urba\’nski in which we extend the theory of thermodynamic formalisms for entire functions far beyond the existing setting. The key point is that we introduce an integral means spectrum for logarithmic tracts which takes care of the fractal behavior of the boundary of the tract near infinity. It turns out that this spectrum behaves well as soon as the tracts have some sufficiently nice geometry which, for example, is the case for quasicircle, John or H\"older tracts. In this case we get a good control of the corresponding transfer operators, leading to full thermodynamic formalism along with its applications.

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