G‐odometers and their almost one‐to‐one extensions
By María Isabel Cortez, S. Petite. 2006
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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.
Subfields: Computer Vision and Pattern Recognition, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c5a877b4018c461635108f41c378dec960d15d5b
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In Computer Vision and Pattern Recognition
In Mathematical Physics
Citations in the corpus
- Weak forms of topological and measure-theoretical equicontinuity: relationships with discrete spectrum and sequence entropy (2014, background): “Toeplitz subshifts are precisely the minimal subshifts that are almost one–one extensions of odometers (for Z+-actions, see [9]; for finitely generated discrete group actions, see [8]).”