1 results
Automorphisms of
${\mathcal B}$-free and other Toeplitz shifts
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 44 / Issue 4 / April 2024
- Published online by Cambridge University Press:
- 13 June 2023, pp. 1058-1101
- Print publication:
- April 2024
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- Article
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We present sufficient conditions for the triviality of the automorphism group of regular Toeplitz subshifts and give a broad class of examples from the class of
${\mathcal B}$-free subshifts satisfying them, extending the work of Dymek [Automorphisms of Toeplitz 
${\mathcal B}$-free systems. Bull. Pol. Acad. Sci. Math. 65(2) (2017), 139–152]. Additionally, we provide an example of a 
${\mathcal B}$-free Toeplitz subshift whose automorphism group has elements of arbitrarily large finite order, answering Question 11 of S. Ferenczi et al [Sarnak’s conjecture: what’s new. Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics (Lecture Notes in Mathematics, 2213). Eds. S. Ferenczi, J. Kułaga-Przymus and M. Lemańczyk. Springer, Cham, 2018, pp. 163–235].
