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Eigenvalues and strong orbit equivalence

Published online by Cambridge University Press:  21 July 2015

MARÍA ISABEL CORTEZ ,
FABIEN DURAND  and
SAMUEL PETITE
MARÍA ISABEL CORTEZ
Affiliation:
Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencia, Universidad de Santiago de Chile, Av. Libertador Bernardo O’Higgins 3363, Santiago, Chile email [email protected] Fédération de Recherche ARC Mathématiques, CNRS-FR 3399, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, France
FABIEN DURAND
Affiliation:
Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS-UMR 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, France email [email protected], [email protected]
SAMUEL PETITE
Affiliation:
Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS-UMR 7352, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, France email [email protected], [email protected]
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Abstract

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 with $(X,T)$ 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 8 , December 2016 , pp. 2419 - 2440
Copyright
© Cambridge University Press, 2015 

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