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H 1 Limits of geodesic push-forwards of horocycle measures

Auteurs : Forni, Giovanni (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We prove a couple of general conditional convergence results on ergodic averages for horocycle and geodesic subgroups of any continuous $SL(2,\mathbb{R})$- action on a locally compact space. These results are motivated by theorems of Eskin, Mirzakhani and Mohammadi on the $SL(2,\mathbb{R})$-action on the moduli space of Abelian differentials. By our argument we can derive from these theorems an improved version of the “weak convergence” of push-forwards of horocycle measures under the geodesic flow and a new short proof of a theorem of Chaika and Eskin on Birkhoff genericity in almost all directions for the Teichmüller geodesic flow.

    Codes MSC :
    37A17 - Homogeneous flows
    37C40 - Smooth ergodic theory, invariant measures
    37D40 - Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 28/02/2017
      Date de captation : 16/02/2017
      Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations
      Format : MP4
      Durée : 00:54:34
      Domaine : Dynamical Systems & ODE
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-02-16_Forni.mp4

    Informations sur la rencontre

    Nom de la rencontre : Espace de Teichmüller. Billards polygonaux, échanges d'intervalles / Teichmüller Space, Polygonal Billiard, Interval Exchanges
    Organisateurs de la rencontre : Chaika, Jon ; Hubert, Pascal ; Lanneau, Erwan ; Skripchenko, Alexandra ; Zorich, Anton
    Dates : 13/02/2017 - 17/02/2017
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1713.html

    Citation Data

    DOI : 10.24350/CIRM.V.19120703
    Cite this video as: Forni, Giovanni (2017). Limits of geodesic push-forwards of horocycle measures. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19120703
    URI : http://dx.doi.org/10.24350/CIRM.V.19120703


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