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Bowen, Lewis Phylip

A measure-conjugacy invariant for free group actions. (English) Zbl 1201.37007

Ann. Math. (2) 171, No. 2, 1387-1400 (2010).
The paper is concerned with the problem of isomorphism of two dynamical systems. D. S. Ornstein and B. Weiss [J. Anal. Math. 48, 1–141 (1987; Zbl 0637.28015)] posed a question regarding the isomorphism of all Bernoulli shifts over a nonamenable group. Using a new measure-conjugacy invariant for actions of free groups, the author shows that two Bernoulli shifts over a finitely generated free group are measurably conjugate if and only if their base measures have the same entropy, thus answering the above question in the negative.
Reviewer: Yuri V. Rogovchenko (Umeå)

Cited in 4 Reviews
Cited in 42 Documents

MSC:

37A35 Entropy and other invariants, isomorphism, classification in ergodic theory

Keywords:

dynamical systems; isomorphism; Bernoulli systems; measurable conjugacy

Citations:

Zbl 0637.28015
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Full Text: DOI arXiv Link

References:

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