TITLE

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

AUTHOR(S)
Cortez, Maráa Isabel; Petite, Samuel
PUB. DATE
August 2008
SOURCE
Journal of the London Mathematical Society;Aug2008, Vol. 78 Issue 1, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
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 = ℤ. 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.
ACCESSION #
44398866

 

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