Ergodic Theory and Dynamical Systems



Affable equivalence relations and orbit structure of Cantor dynamical systems


THIERRY GIORDANO a1, IAN PUTNAM a2 and CHRISTIAN SKAU a3
a1 Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Canada K1N 6N5 (e-mail: giordano@uottawa.ca)
a2 Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada V8W 3P4 (e-mail: putnam@math.uvic.ca)
a3 Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO–7491 Trondheim, Norway (e-mail: csk@math.ntnu.no)

Article author query
giordano t   [Google Scholar] 
putnam i   [Google Scholar] 
skau c   [Google Scholar] 
 

Abstract

We prove several new results about AF-equivalence relations and relate these to Cantor minimal systems (i.e. to minimal Z-actions). The results we obtain turn out to be crucial for the study of the topological orbit structure of more general countable group actions (as homeomorphisms) on Cantor sets, which will be the topic of a forthcoming paper. In all this, Bratteli diagrams and their dynamical interpretation are indispensable tools.

(Received April 29 2002)
(Revised March 19 2003)