Characterizing mildly mixing actions by orbit equivalence of products.
Hawkins, Jane, Silva Cesar, E. (1998)
The New York Journal of Mathematics [electronic only]
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Displaying similar documents to “Orbit coupling”
Characterizing mildly mixing actions by orbit equivalence of products.
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The orbit equivalence of type ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type cocycles with values in Abelian groups.
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We prove a strengthened version of Dye's theorem on orbit equivalence, showing that if the transformation structures are represented as finite coordinate change equivalence relations of ergodic measured Bratteli diagrams, then there is a finitary orbit equivalence between these diagrams.