Skip to main content
    • Aa
    • Aa

Finite-rank Bratteli–Vershik diagrams are expansive


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.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[2] M. Cortez , F. Durand , B. Host and A. Maass . Continuous and measurable eigenfunctions of linearly recurrent dynamical Cantor systems. J. London Math. Soc. 67 (2003), 790804.

[3] F. Durand . Linearly recurrent subshifts have a finite number of non-periodic subshift factors. Ergod. Th. & Dynam. Sys. 20 (2000), 10611078.

[4] F. Durand , B. Host and C. Skau . Substitutional dynamical systems, Bratteli diagrams and dimension groups. Ergod. Th. & Dynam. Sys. 19 (1999), 953993.

[6] R. Gjerde and O. Johansen . Bratteli–Vershik models for Cantor minimal systems: Applications to Toeplitz flows. Ergod. Th. & Dynam. Sys. 20 (2000), 16871710.

[7] G. A. Hedlund . Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3 (1969), 320375.

[8] R. Herman , I. Putnam and C. Skau . Ordered Bratteli diagrams, dimension groups and topological dynamics. Internat. J. Math. 3 (1992), 827864.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 9 *
Loading metrics...

Abstract views

Total abstract views: 53 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 28th May 2017. This data will be updated every 24 hours.