학술논문

Automorphisms of $\Cal B$-free and other Toeplitz shifts.
Document Type
Journal
Author
Dymek, Aurelia (PL-TORNM) AMS Author Profile; Kasjan, Stanisław (PL-TORNM) AMS Author Profile; Keller, Gerhard (D-ERL) AMS Author Profile
Source
Ergodic Theory and Dynamical Systems (Ergodic Theory Dynam. Systems) (20240101), 44, no.~4, 1058-1101. ISSN: 0143-3857 (print).eISSN: 1469-4417.
Subject
37 Dynamical systems and ergodic theory -- 37B Topological dynamics
  37B05 Transformations and group actions with special properties
Language
English
Abstract
This paper continues a rich line of research into the automorphism group of Toeplitz subshifts, which are objects of fundamental importance in symbolic dynamics. The authors establish conditions under which the automorphism group of regular Toeplitz subshifts is trivial. They provide numerous examples from the class of $\Cal{B}$-free subshifts that meet these conditions, building upon the work of A. Dymek [Bull. Pol. Acad. Sci. Math. {\bf 65} (2017), no.~2, 139--152; MR3731019]. Additionally, they present an example of a $\Cal{B}$-free Toeplitz subshift with an automorphism group containing elements of arbitrarily large finite order, addressing Question 11, posed by S. Ferenczi, J. Kułaga-Przymus and M. Lemańczyk [in {\it Ergodic theory and dynamical systems in their interactions with arithmetics and combinatorics}, 163--235, Lecture Notes in Math., 2213, Springer, Cham, 2018; MR3821717].