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Smooth, mixing transformations with loosely Bernoulli Cartesian square
Published online by Cambridge University Press: 04 June 2021
Abstract
A zero-entropy system is said to be loosely Bernoulli if it can be induced from an irrational rotation of the circle. We provide a criterion for zero-entropy systems to be loosely Bernoulli that is compatible with mixing. Using this criterion, we show the existence of smooth mixing zero-entropy loosely Bernoulli transformations whose Cartesian square is loosely Bernoulli.
- Type
- Original Article
- Information
- Ergodic Theory and Dynamical Systems , Volume 42 , Issue 3: Anatole Katok Memorial Issue Part 2: Special Issue of Ergodic Theory and Dynamical Systems , March 2022 , pp. 1252 - 1283
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press