Characterizations of periods of multidimensional shifts

Abstract : We show that the sets of periods of multidimensional shifts of finite type (SFTs) are exactly the sets of integers of the complexity class $\NE$. We also show that the functions counting their number are the functions of $\#\E$. We also give characterizations of some other notions of periodicity. We finish the paper by giving some characterizations for sofic and effective subshifts.
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Emmanuel Jeandel, Pascal Vanier. Characterizations of periods of multidimensional shifts. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2015, 35 (2), pp.431--460. ⟨10.1017/etds.2013.60⟩. ⟨hal-00798336⟩

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