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Affable equivalence relations and orbit structure of Cantor dynamical systems

Published online by Cambridge University Press:  09 March 2004

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

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 2 , April 2004, pp. 441 - 475
Copyright
2004 Cambridge University Press