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H 1 Some remarks regarding ergodic operators

Auteurs : Matheron, Etienne (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Let us say that a continuous linear operator $T$ acting on some Polish topological vector space is ergodic if it admits an ergodic probability measure with full support. This talk will be centred in the following question: how can we see that an operator is or is not ergodic? More precisely, I will try (if I’m able to manage my time) to talk about two “positive" results and one “negative" result. The first positive result says that if the operator $T$ acts on a reflexive Banach space and satisfies a strong form of frequent hypercyclicity, then $T$ is ergodic. The second positive result is the well-known criterion for ergodicity relying on the perfect spanning property for unimodular eigenvectors, of which I will outline a “soft" Baire category proof. The negative result will be stated in terms of a parameter measuring the maximal frequency with which (generically) the orbit of a hypercyclic vector for $T$ can visit a ball centred at 0. The talk is based on joint work with Sophie Grivaux.

    Codes MSC :
    37A05 - Measure-preserving transformations
    47A16 - Cyclic vectors, hypercyclic and chaotic operators
    47A35 - Ergodic theory of linear operators

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 03/11/15
      Date de captation : 01/10/15
      Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations
      Format : MP4
      Durée : 00:53:30
      Domaine : Dynamical Systems & ODE
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-10-01_Matheron.mp4

    Informations sur la rencontre

    Nom de la rencontre : Frontiers of operator dynamics / Frontières de la dynamique linéaire
    Organisateurs de la rencontre : Grivaux, Sophie ; Lemanczyk, Marius ; Tomilov, Yuri
    Dates : 28/09/15 - 02/10/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1125.html

    Citation Data

    DOI : 10.24350/CIRM.V.18844203
    Cite this video as: Matheron, Etienne (2015). Some remarks regarding ergodic operators. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18844203
    URI : http://dx.doi.org/10.24350/CIRM.V.18844203


    Bibliographie

    1. Grivaux, S., & Matheron, E. (2014). Invariant measures for frequently hypercyclic operators. Advances in Mathematics, 265, 371-427 - http://dx.doi.org/10.1016/j.aim.2014.08.002

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