## GT ADG-Systèmes Dynamiques

**Generalized integral means spectrum**

Michel Zinsmeister

Tuesday 03 March 2015 14:00 - Orléans - Salle PTICREM

**Résumé :**

the multifractal spectrum of harmonic measure on a bounded simply-connected domain in the plane is related via a Legendre transform to the spectrum of integral means of the derivative of the Riemann mapping. This spectrum makes sense even if the domain is unbounded but the associated universal spectrum for bounded or unbounded functions is not the same. In a recent work by B.Duplantier, Ho Xuan Hieu, Le Thanh Binh and myself we have introduced a new spectrum with two parameters for the whole plane SLE that allow to unify the bounded and unbounded case. In this talk I will show how this new spectrum can be used to have a unified description of the universal case, and maybe help to solve the resisting conjectures about universal spectrum (like Brennan conjecture). This is a work in progress with K.Astala, B.Duplantier and myself.

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