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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2021

The expressiveness of quasiperiodic and minimal shifts of finite type

Résumé

We study multidimensional minimal and quasiperiodic shifts of finite type. We prove for these classes several results that were previously known for the shifts of finite type in general, without restriction. We show that some quasiperiodic shifts of finite type admit only non-computable configurations; we characterize the classes of Turing degrees that can be represented by quasiperiodic shifts of finite type. We also transpose to the classes of minimal/quasiperiodic shifts of finite type some results on subdynamics previously known for the effective shifts without restrictions: every effective minimal (quasiperiodic) shift of dimension $d$ can be represented as a projection of a subdynamics of a minimal (respectively, quasiperiodic) shift of finite type of dimension $d+1$.
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Dates et versions

hal-01702549 , version 1 (20-12-2019)

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Bruno Durand, Andrei Romashchenko. The expressiveness of quasiperiodic and minimal shifts of finite type. Ergodic Theory and Dynamical Systems, 2021, 41 (4), pp.1086-1138. ⟨10.1017/etds.2019.112⟩. ⟨hal-01702549⟩
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