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Smooth, mixing transformations with loosely Bernoulli Cartesian square

Part of: Smooth dynamical systems: general theory Ergodic theory

Published online by Cambridge University Press:  04 June 2021

FRANK TRUJILLO Open the ORCID record for FRANK TRUJILLO [Opens in a new window]
FRANK TRUJILLO*
Affiliation:
CNRS, IMJ-PRG, Institut de Mathématiques de Jussieu, UMR7586 Bâtiment Sophie Germain, 75205Paris Cedex 13, France
*
e-mail: [email protected]
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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.

Keywords

classical ergodic theoryclassification in ergodic theorysmooth dynamics

MSC classification

Primary: 37A05: Measure-preserving transformations 37A35: Entropy and other invariants, isomorphism, classification
Secondary: 37C05: Smooth mappings and diffeomorphisms 37C10: Vector fields, flows, ordinary differential equations
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
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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