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H 1 Yet another characterization of the Pisot conjecture

Auteurs : Mercat, Paul (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In the way of Arnoux-Ito, we give a general geometric criterion for a subshift to be measurably conjugated to a domain exchange and to a translation on a torus. For a subshift coming from an unit Pisot irreducible substitution, we will see that it becomes a simple topological criterion. More precisely, we define a topology on $\mathbb{Z}^d$ for which the subshift has pure discrete spectrum if and only if there exists a domain of the domain exchange on the discrete line that has non-empty interior. We will see how we can compute exactly such interior using regular languages. This gives a way to decide the Pisot conjecture for any example of unit Pisot irreducible substitution.
    Joint work with Shigeki Akiyama.

    Codes MSC :
    11A63 - Radix representation; digital problems
    28A80 - Fractals
    37B10 - Symbolic dynamics
    68R15 - Combinatorics on words

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 07/12/2017
      Date de captation : 06/12/2017
      Collection : Research talks ; Computer Science ; Dynamical Systems and Ordinary Differential Equations ; Number Theory
      Format : MP4
      Durée : 00:55:32
      Domaine : Number Theory ; Dynamical Systems & ODE ; Computer Science
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-12-06_Mercat.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean-Morlet chair: Tiling and recurrence / Chaire Jean-Morlet : Pavages et récurrence
    Organisateurs de la rencontre : Akiyama, Shigeki ; Arnoux, Pierre
    Dates : 04/12/2017 - 08/12/2017
    Année de la rencontre : 2017
    URL Congrès : https://akiyama-arnoux.weebly.com/conference.html

    Citation Data

    DOI : 10.24350/CIRM.V.19250103
    Cite this video as: Mercat, Paul (2017). Yet another characterization of the Pisot conjecture. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19250103
    URI : http://dx.doi.org/10.24350/CIRM.V.19250103

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