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Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

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Orbit equivalence for Cantor minimal systems
by
Ian Putnam
University of Victoria
Coauthors: Thierry Giordano (Ottawa), Hiroki Matui (Ciba), Christian Skau (Trondheim)

We discuss minimal Cantor systems; that is, actions of discrete groups on a compact, totally disconnected metrizable space in which every orbit is dense. Following Dye's work in ergodic theory, we say that two such systems are orbit equivalent if there is a homeomorphism between the underlying spaces which carries orbits to orbits. We introduce an invariant which is an ordered abelian group. If the action has a single invariant measure, this amounts to the measures of the clopen subsets. For actions of Zd, this is a complete invariant. The main tool is to find locally finite approximations to the orbit structure; these are called AF-relations and play the role in the topological setting of Rohlin partititons in the ergodic case.

Date received: January 7, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawk-14.