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Flow–orbit equivalence for minimal Cantor systems

Published online by Cambridge University Press:  01 April 2008

WOJCIECH KOSEK ,
NICHOLAS ORMES  and
DANIEL J. RUDOLPH
WOJCIECH KOSEK
Affiliation:
Mathematics Department, Colorado College, 14 E. Cache La Poudre, Colorado Springs, CO 80903, USA (email: wkosek@coloradocollege.edu)
NICHOLAS ORMES
Affiliation:
Mathematics Department, University of Denver, 2360 S. Gaylord St., Denver, CO 80208, USA (email: normes@math.du.edu)
DANIEL J. RUDOLPH
Affiliation:
Mathematics Department, Colorado State University, Fort Collins, CO 80523-1874, USA (email: rudolphd@math.colostate.edu)
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Abstract

This paper is about flow–orbit equivalence, a topological analog of even Kakutani equivalence. In addition to establishing many basic facts about this relation, we characterize the conjugacies of induced systems that can be extended to a flow–orbit equivalence. We also describe the relationship between flow–orbit equivalence and a distortion function of an orbit equivalence. We show that, if the distortion of an orbit equivalence is zero, then it is in fact a flow–orbit equivalence, and that the converse is true up to a conjugation by an element of the full group.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 2: William Parry Memorial Volume , April 2008 , pp. 481 - 500
Copyright
Copyright © Cambridge University Press 2008

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