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A  counterexample machine
Author:
Christopher Hoffman
Journal:
Trans. Amer. Math. Soc. 351 (1999), 4263-4280
MSC (1991):
Primary 28D05; Secondary 28D20
Posted:
July 1, 1999
MathSciNet review:
1650089
Full-text PDF Free Access
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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:
http://dx.doi.org/10.1090/S0002-9947-99-02446-0
PII:
S 0002-9947(99)02446-0
Received by editor(s):
March 31, 1997
Posted:
July 1, 1999
Article copyright:
© Copyright 1999 American Mathematical Society
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