Finite-rank Bratteli–Vershik diagrams are expansive
By Tomasz Downarowicz, Alejandro Maass. Ergodic Theory and Dynamical Systems, 2008
75 citations recorded by the source corpus.
Abstract The representation of Cantor minimal systems by Bratteli–Vershik diagrams has been extensively used to study particular aspects of their dynamics. A main role has been played by the symbolic factors induced by the way vertices of a fixed level of the diagram are visited by the dynamics. The main result of this paper states that Cantor minimal systems that can be represented by Bratteli–Vershik diagrams with a uniformly bounded number of vertices at each level (called finite-rank systems) are either expansive or topologically conjugate to an odometer. More precisely, when expansive, they are topologically conjugate to one of their symbolic factors.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f6ce70e23860f8a852542426cc7424591f1a1678
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Citations in the corpus
- Aperiodic substitution systems and their Bratteli diagrams (2007, methodology): “In the section, we develop the ideas of the paper [DM] and apply them below to solving the following problems: recognizability of aperiodic substitutions (Section 5) and expansiveness of Vershik maps (Section 4). The results stated in this section are proved in [ DM ].”
- Finite rank Bratteli diagrams: Structure of invariant measures (2010, background): “Morse sequences (Example 4.16) belong to this class of systems [DHS99], [BKM09], [GJ02]. Conversely, every Vershik map on a finite rank diagram is either an odometer or a subshift on a finite alphabet ([DM08], [BKM09]). However, to the best of our knowledge, it is still unknown what kind of subshifts ”