A 𝐾 counterexample machine

Hoffman, Christopher

doi:10.1090/S0002-9947-99-02446-0

A $K$ counterexample machine
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by Christopher Hoffman PDF

Trans. Amer. Math. Soc. 351 (1999), 4263-4280 Request permission

Abstract:

We present a general method for constructing families of measure preserving transformations which are $K$ and loosely Bernoulli with various ergodic theoretical properties. For example, we construct two $K$ transformations which are weakly isomorphic but not isomorphic, and a $K$ 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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