Families of type III<inf>0</inf> ergodic transformations in distinct orbit equivalent classes

Publication Type:
Journal Article
Citation:
Monatshefte fur Mathematik, 2011, 164 (4), pp. 369 - 381
Issue Date:
2011-12-01
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A new isomorphism invariant of certain measure preserving flows, using sequences of integers, is introduced. Using this invariant, we are able to construct large families of type III 0 systems which are not orbit equivalent. In particular we construct an uncountable family of nonsingular ergodic transformations, each having an associated flow that is approximately transitive (and therefore of zero entropy), with the property that the transformations are pairwise not orbit equivalent. © 2011 Springer-Verlag.
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