• D

F Nous contacter

0

# Multi angle

O

Multi angle Automorphism groups of low complexity subshift - Lecture 2

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

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 Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 08/12/16 Date de captation : 29/11/16 Collection : Research schools Format : MP4 Durée : 01:06:42 Domaine : Dynamical Systems & ODE ; Computer Science Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctorants , Post - Doctorants Download : http://videos.cirm-math.fr/2016-11-29_Petite.mp4 Informations sur la rencontre Nom du congrès : Combinatorics, automata and number theory / Combinatoire, automates et théorie des nombresOrganisteurs Congrès : Berthé, Valérie ; Rigo, MichelDates : 28/11/16 - 02/12/16 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1502.htmlCitation DataDOI : 10.24350/CIRM.V.19098003Cite this video as: Petite, Samuel (2016). Automorphism groups of low complexity subshift - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19098003URI : http://dx.doi.org/10.24350/CIRM.V.19098003

### Voir aussi

Bibliographie

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

Z