Reparametrization of -flows of zero entropy

Authors:
J. Feldman and D. Nadler

Journal:
Trans. Amer. Math. Soc. **256** (1979), 289-304

MSC:
Primary 28D15

MathSciNet review:
546919

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Abstract: Let , be two ergodic *n*-parameter flows which preserve finite probability measures on their spaces *X*, *Y*. Let *T* be a nullset-preserving map: sending each -orbit homeomorphically to a -orbit. Then , are called homeomorphically orbit-equivalent. For , there has been developed a theory of such equivalence: ``Loosely Bernoulli'' theory. A completely parallel theory exists for higher dimensions, except that it is necessary to impose a certain natural ``growth'' restriction on *T*, a restriction which is vacuous in the case . In this paper we carry out this program, but only for the case of zero entropy.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1979-0546919-6

Article copyright:
© Copyright 1979
American Mathematical Society