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classification in ergodic theory

Ergodic Theory and Dynamical Systems (1)

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Smooth, mixing transformations with loosely Bernoulli Cartesian square
Part of
- Ergodic theory
- Smooth dynamical systems: general theory
FRANK TRUJILLO
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 3 / March 2022

Published online by Cambridge University Press:

04 June 2021, pp. 1252-1283

Print publication:

March 2022
- Article
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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.