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Agenda ERC IChaos

par Lozingot Eric, Teychene Romain - publié le , mis à jour le

Agenda

Séminaire

groupe de travail

  • Vendredi 19 octobre 09:30-10:30 - Alexey KLIMENKO - Steklov Mathematical Institute of RAS & NRU Higher School of Economics, Moscow, Russia

    Convergence of spherical averages for actions of Fuchsian groups

    Résumé : Consider a measure-preserving action of a Fuchsian group G on a Lebesgue probability space X. Given a fundamental domain R, we obtain a symmetric generating set consisting of all group elements that map R to adjacent domains. This generating set endows the group G with the norm, and for a function f on X, we define its spherical average of order n as the average with equal weights of f shifted by all elements in G with the norm n.
    Assume now that R has even corners, that is, that for the tessellation of the hyperbolic plane by images of R the boundaries between domains comprise of complete geodesic lines. Our result now says that if the even corners condition holds, then for any L^p-function f, p>1, its spherical averages of even orders converge almost surely.
    The main ingredient of the proof is the construction of the new Markov coding for a Fuchsian group with the even corners condition. The key property of our coding is the following symmetry condition : the sequence of states generating an element g^-1 is obtained from the sequence for g as follows : we reverse the order of its terms and apply an involution on the state space to each of these terms.
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    The talk is based on the joint work with A. Bufetov and C. Series (arXiv:1805.11743).
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    JPEG - 10.2 ko
    Alexey KLIMENKO

    Lieu : FRUMAM - Aix-Marseille Université - Site St Charles
    3, place Victor Hugo - case 39
    13331 MARSEILLE Cedex 03

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