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- W4287979040 abstract "M. Foreman and B. Weiss obtained an anti-classification result for smooth ergodic diffeomorphisms, up to measure isomorphism, by using a functor $mathcal{F}$ mapping odometer-based systems, $mathcal{OB}$, to circular systems, $mathcal{CB}$. This functor transfers the classification problem from $mathcal{OB}$ to $mathcal{CB}$, and it preserves weakly mixing extensions, compact extensions, factor maps, the rank-one property, and certain types of isomorphisms. Thus it is natural to ask whether $mathcal{F}$ preserves other dynamical properties. We show that $mathcal{F}$ does not preserve the loosely Bernoulli property by providing positive and zero entropy examples of loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli. We also construct a loosely Bernoulli circular system whose corresponding odometer-based system has zero entropy and is not loosely Bernoulli." @default.
- W4287979040 created "2022-07-26" @default.
- W4287979040 creator A5054670548 @default.
- W4287979040 creator A5081660382 @default.
- W4287979040 date "2019-12-29" @default.
- W4287979040 modified "2023-09-27" @default.
- W4287979040 title "Loosely Bernoulli Odometer-Based Systems Whose Corresponding Circular Systems Are Not Loosely Bernoulli" @default.
- W4287979040 doi "https://doi.org/10.48550/arxiv.1912.12684" @default.
- W4287979040 hasPublicationYear "2019" @default.
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