ON AUTOMORPHISM GROUPS OF LOW COMPLEXITY MINIMAL SUBSHIFTS

Autor: Sebastian Donoso, Fabien Durand, Alejandro Maass, Samuel Petite
Přispěvatelé: Universidad de Santiago de Chile [Santiago] (USACH), Communauté Université Paris-Est, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA), Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS), Centre de Modélisation Mathématique / Centro de Modelamiento Matemático (CMM), Centre National de la Recherche Scientifique (CNRS), Centro de Regulación Génica (CRG), Pontificia Universidad Católica de Chile (UC)-Universidad Andrés Bello [Santiago] (UNAB), This research was partially supported by grants Basal-CMM \& Fondap 15090007, CONICYT Doctoral fellowship 21110300, ANR SubTile and the cooperation project MathAmSud DYSTIL. The first and third authors thanks University of Picardie Jules Verne where this research was finished.
Jazyk: angličtina
Rok vydání: 2016
Předmět:
Zdroj: Ergodic Theory and Dynamical Systems
Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2016
HAL
ISSN: 0143-3857
1469-4417
Popis: International audience; In this article we study the automorphism group Aut(X, σ) of a minimal subshift (X, σ) of low word complexity. In particular, we prove that Aut(X, σ) is virtually Z for aperiodic minimal subshifts with affine complexity on a subsequence, more precisely, the quotient of this group by the one gen-erated by the shift map is a finite group. In addition, we provide examples to show that any finite group can be obtained in this way. The class con-sidered includes minimal substitutions, linearly recurrent subshifts and even some minimal subshifts with polynomial complexity. In the case of polyno-mial complexity, first we prove that for minimal subshifts with polynomial recurrence any finitely generated subgroup of Aut(X, σ) is virtually nilpotent. Then, we describe several subshifts of polynomial complexity to illustrate that the group of automorphisms can still be virtually Z. This behavior seems to be very frequent for low complexity minimal subshifts. The main technique in this article relies on the study of classical relations among points used in topological dynamics, in particular asymptotic pairs.
Databáze: OpenAIRE