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H 1 Automorphism groups of low complexity subshift - Lecture 2

Auteurs : Petite, Samuel (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : An automorphism of a subshift $X$ is a self-homeomorphism of $X$ that commutes with the shift map. The study of these automorphisms started at the very beginning of the symbolic dynamics. For instance, the well known Curtis-Hedlund-Lyndon theorem asserts that each automorphism is a cellular automaton. The set of automorphisms forms a countable group that may be very complicated for mixing shift of finite type (SFT). The study of this group for low complexity subshifts has become very active in the last five years. Actually, for zero entropy subshift, this group is much more tame than in the SFT case. In a first lecture we will recall some striking property of this group for subshift of finite type. The second lecture is devoted to the description of this group for classical minimal sub shifts of zero entropy with sublinear complexity and for the family of Toeplitz subshifts. The last lecture concerns the algebraic properties of the automorphism group for subshifts with sub-exponential complexity. We will also explain why sonic group like the Baumslag-Solitar $BS(1,n)$ or $SL(d,Z), d >2$, can not embed into an automorphism group of a zero entropy subshift.

    Codes MSC :
    37B10 - Symbolic dynamics
    37B15 - Cellular automata
    37B50 - Multi-dimensional shifts of finite type, tiling dynamics
    68Q80 - Cellular automata (theory of computing)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 08/12/16
      Date de captation : 29/11/16
      Collection : Research schools ; Computer Science ; Dynamical Systems and Ordinary Differential Equations
      Format : MP4
      Durée : 01:06:42
      Domaine : Dynamical Systems & ODE ; Computer Science
      Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2016-11-29_Petite.mp4

    Informations sur la rencontre

    Nom de la rencontre : Combinatorics, automata and number theory / Combinatoire, automates et théorie des nombres
    Organisateurs de la rencontre : Berthé, Valérie ; Rigo, Michel
    Dates : 28/11/16 - 02/12/16
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1502.html

    Citation Data

    DOI : 10.24350/CIRM.V.19098003
    Cite this video as: Petite, Samuel (2016). Automorphism groups of low complexity subshift - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19098003
    URI : http://dx.doi.org/10.24350/CIRM.V.19098003

    Voir aussi


    1. Donoso, S., Durand, F., Maass, A., & Petite, S. (2016). On automorphism groups of low complexity subshifts. Ergodic Theory and Dynamical Systems, 36(1), 64-95 - http://dx.doi.org/10.1017/etds.2015.70

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