00:00:00 / 00:00:00

Automorphism groups of low complexity subshift - Lecture 2

By Samuel Petite

Appears in collections : Combinatorics, automata and number theory / Combinatoire, automates et théorie des nombres, Ecoles de recherche

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.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19098003
  • Cite this video Petite, Samuel (29/11/2016). Automorphism groups of low complexity subshift - Lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19098003
  • URL https://dx.doi.org/10.24350/CIRM.V.19098003



  • 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

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow


  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
  • Get notification updates
    for your favorite subjects
Give feedback
Loading the web debug toolbar…
Attempt #