A zero-entropy mixing transformation whose product with itself is loosely Bernoulli

DOI10.1007/BF02761843zbMath0458.28015OpenAlexW2078661714MaRDI QIDQ1151473

Marlies Gerber

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1007/bf02761843

zbMATH Keywords

entropymixingKakutani equivalencecutting and stackingvery weak Bernoulliloosely BernoulliVersik property

Mathematics Subject Classification ID

Measure-preserving transformations (28D05)

Related Items (6)

A $K$ counterexample machine ⋮ Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrödinger equations ⋮ A smooth zero-entropy diffeomorphism whose product with itself is loosely Bernoulli ⋮ Product of two staircase rank one transformations that is not loosely Bernoulli ⋮ A loosely Bernoulli counterexample machine ⋮ Smooth, mixing transformations with loosely Bernoulli Cartesian square

Cites Work

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• Horocycle flows are loosely Bernoulli
• The Cartesian square of the horocycle flow is not loosely Bernoulli
• Versik processes: First steps
• New \(K\)-automorphisms and a problem of Kakutani
• Standardness of automorphisms of transposition of intervals and fluxes on surfaces
• Loosely Bernoulli Cartesian Products
• MONOTONE EQUIVALENCE IN ERGODIC THEORY
• AN INVARIANT OF MONOTONE EQUIVALENCE DETERMINING THE QUOTIENTS OF AUTOMORPHISMS MONOTONELY EQUIVALENT TO A BERNOULLI SHIFT

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