The Cartesian square of the horocycle flow is not loosely Bernoulli

DOI10.1007/BF02761825zbMath0437.28010OpenAlexW2025982248MaRDI QIDQ1141250

Marina Ratner

Publication date: 1979

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02761825

zbMATH Keywords

Cartesian squareKakutani equivalencehorocycle flownon-loosely Bernoulli transformations

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) One-parameter continuous families of measure-preserving transformations (28D10)

Related Items (17)

New time-changes of unipotent flows on quotients of Lorentz groups ⋮ Slow entropy for some smooth flows on surfaces ⋮ On topological models of zero entropy loosely Bernoulli systems ⋮ Time change for unipotent flows and rigidity ⋮ Rigidity of joinings for time changes of unipotent flows on quotients of Lorentz groups ⋮ A zero-entropy mixing transformation whose product with itself is loosely Bernoulli ⋮ Smooth non-Bernoulli k-automorphisms ⋮ Rigidity of time changes for horocycle flows ⋮ Some invariants of Kakutani equivalence ⋮ On the non-equivalence of the Bernoulli and \(K\) properties in dimension four ⋮ Time change invariants for measure preserving flows ⋮ A smooth zero-entropy diffeomorphism whose product with itself is loosely Bernoulli ⋮ Kakutani equivalence of unipotent flows ⋮ Product of two staircase rank one transformations that is not loosely Bernoulli ⋮ Kakutani equivalence for products of some special flows over rotations ⋮ Loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli ⋮ Smooth, mixing transformations with loosely Bernoulli Cartesian square

Cites Work

• Unnamed Item
• Classifying the isometric extensions of a Bernoulli shift
• Horocycle flows are loosely Bernoulli
• Unique ergodicity of the horocycle flow: variable negative curvature case
• New \(K\)-automorphisms and a problem of Kakutani
• Unique ergodicity for horocycle foliations
• The horocycle flow is mixing of all degrees
• Certain measures associated with U-flows on compact manifolds
• Flows on some three dimensional homogeneous spaces
• Loosely Bernoulli Cartesian Products
• Equivalence of measure preserving transformations
• SOME SMOOTH ERGODIC SYSTEMS

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