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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2016

Eigenvalues and strong orbit equivalence

Résumé

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 minimal Cantor system (X,T) is a subgroup of the intersection I(X,T) of all the images of the dimension group by its traces. We show, whenever the infinitesimal subgroup of the dimension group associated to (X,T) is trivial, the quotient group I(X,T)/E(X,T) is torsion free. We give examples with non trivial infinitesimal subgroups where this property fails. We also provide some realization results.
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Dates et versions

hal-01053638 , version 1 (31-07-2014)

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Maria Isabel Cortez, Fabien Durand, Samuel Petite. Eigenvalues and strong orbit equivalence. Ergodic Theory and Dynamical Systems, 2016, ⟨10.1017/etds.2015.26⟩. ⟨hal-01053638⟩
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