Dimension and infinitesimal groups of Cantor minimal systems

Jan Kwiatkowski, Marcin Wata

DOI: http://dx.doi.org/10.12775/TMNA.2004.008

Abstract


The dimension and infinitesimal groups of a Cantor dynamical
system $(X,T)$ are inductive limits of sequences of homomorphisms
defined by a proper Bratteli diagram of $(X,T)$. A method of selecting
sequences of homomorphisms determining the dimension and the infinitesimal
groups of $(X,T)$ based on non-proper Bratteli diagrams is described.
The dimension and infinitesimal groups of Rudin-Shapiro,
Morse and Chacon flows are computed.

Keywords


Bratteli diagrams; Dimension groups; Kakutani-Rokhlin partitions

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