G-odometers and their almost one-to-one extensions

• Autores: María Isabel Cortez, Samuel Petite
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 78, Nº 1, 2008, págs. 1-20
• Idioma: inglés
• DOI: 10.1112/jlms/jdn002
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• Resumen

  • In this paper we recall the concepts of G-odometers and G-subodometers for G-actions, where G is a discrete finitely generated group; these generalize the notion of an odometer in the case G = . We characterize the G-regularly recurrent systems as the minimal almost one-to-one extensions of subodometers, from which we deduce that the family of the G-Toeplitz subshifts coincides with the family of the minimal symbolic almost one-to-one extensions of subodometers. We determine the continuous eigenvalues of these systems. When G is amenable and residually finite, a characterization of the G-invariant measures of these systems is given.