Interplay between finite topological rank minimal Cantor systems, 𝒮-adic subshifts and their complexity

Autor: Fabien Durand, Samuel Petite, Sebastián Donoso, Alejandro Maass

Publikováno v: Transactions of the American Mathematical Society. 374:3453-3489

Minimal Cantor systems of finite topological rank (that can be represented by a Bratteli-Vershik diagram with a uniformly bounded number of vertices per level) are known to have dynamical rigidity properties. We establish that such systems, when they

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f4ace319a183a43bc084fbc712a3fe92
https://doi.org/10.1090/tran/8315

Realization of big centralizers of minimal aperiodic actions on the Cantor set

Autor: Samuel Petite, María Isabel Cortez

Publikováno v: Discrete & Continuous Dynamical Systems-A
Discrete & Continuous Dynamical Systems-A, 2020, 40 (5), pp.2891-2901. ⟨10.3934/dcds.2020153⟩

In this article we study the centralizer of a minimal aperiodic action of a countable group on the Cantor set (an aperiodic minimal Cantor system). We show that any countable residually finite group is the subgroup of the centralizer of some minimal

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c42bd91b2c58d5b77d80ac6ca6b91684
https://doi.org/10.3934/dcds.2020153

On automorphism groups of low complexity subshifts

Autor: Sebastián Donoso, Samuel Petite, Fabien Durand, Alejandro Maass

Publikováno v: Ergodic Theory and Dynamical Systems. 36:64-95

In this article, we study the automorphism group$\text{Aut}(X,{\it\sigma})$of subshifts$(X,{\it\sigma})$of low word complexity. In particular, we prove that$\text{Aut}(X,{\it\sigma})$is virtually$\mathbb{Z}$for aperiodic minimal subshifts and certain

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ed4f784058f435795bc73d7d732c4498
https://doi.org/10.1017/etds.2015.70

ON THE SIMPLICITY OF HOMEOMORPHISM GROUPS OF A TILABLE LAMINATION

Autor: Samuel Petite, José Aliste-Prieto

Publikováno v: Monatshefte für Mathematik
Monatshefte für Mathematik, Springer Verlag, 2016, 181, pp.285-300. ⟨10.1007/s00605-016-0921-1⟩

We show that the identity component of the group of homeomorphisms that preserve all leaves of a R^d-tilable lamination is simple. Moreover, in the one dimensional case, we show that this group is uniformly perfect. We obtain a similar result for a d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a99c90df20c9f1b081b5f4d298eabd9f
https://hal.archives-ouvertes.fr/hal-01053917

Eigenvalues and strong orbit equivalence

Autor: Samuel Petite, Fabien Durand, María Isabel Cortez

Publikováno v: Ergodic Theory and Dynamical Systems
Artículos CONICYT
CONICYT Chile
instacron:CONICYT
Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2016, ⟨10.1017/etds.2015.26⟩

We give conditions on the subgroups of the circle to be realized as the subgroups of eigenvalues of minimal Cantor systems belonging to a determined strong orbit equivalence class. Actually, the additive group of continuous eigenvalues E(X,T) of the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9d8eb6bc63a14c82246c992bd4c68709