A counterexample machine

Author:
Christopher Hoffman

Journal:
Trans. Amer. Math. Soc. **351** (1999), 4263-4280

MSC (1991):
Primary 28D05; Secondary 28D20

DOI:
https://doi.org/10.1090/S0002-9947-99-02446-0

Published electronically:
July 1, 1999

MathSciNet review:
1650089

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Abstract | References | Similar Articles | Additional Information

Abstract: We present a general method for constructing families of measure preserving transformations which are and loosely Bernoulli with various ergodic theoretical properties. For example, we construct two transformations which are weakly isomorphic but not isomorphic, and a transformation with no roots. Ornstein's isomorphism theorem says families of Bernoulli shifts cannot have these properties. The construction uses a combination of properties from maps constructed by Ornstein and Shields, and Rudolph, and reduces the question of isomorphism of two transformations to the conjugacy of two related permutations.

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Additional Information

**Christopher Hoffman**

Affiliation:
The Hebrew University, Institute of Mathematics, Jerusalem, Israel

Address at time of publication:
Department of Mathematics, University of Maryland, College Park, Maryland 20742

Email:
hoffman@math.umd.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02446-0

Received by editor(s):
March 31, 1997

Published electronically:
July 1, 1999

Article copyright:
© Copyright 1999
American Mathematical Society