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Transactions of the American Mathematical Society

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Reparametrization of $ n$-flows of zero entropy

Authors: J. Feldman and D. Nadler
Journal: Trans. Amer. Math. Soc. 256 (1979), 289-304
MSC: Primary 28D15
Correction: Trans. Amer. Math. Soc. 264 (1981), 583-585.
MathSciNet review: 546919
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Abstract: Let $ \phi $, $ \psi $ be two ergodic n-parameter flows which preserve finite probability measures on their spaces X, Y. Let T be a nullset-preserving map: $ X\, \to \,Y$ sending each $ \phi $-orbit homeomorphically to a $ \phi $-orbit. Then $ \phi $, $ \psi $ are called homeomorphically orbit-equivalent. For $ n\, = \,1$, 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 $ n\, = \,1$. In this paper we carry out this program, but only for the case of zero entropy.

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Article copyright: © Copyright 1979 American Mathematical Society

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