Smooth non-Bernoulli k-automorphisms

DOI10.1007/BF01390069zbMath0467.58016OpenAlexW4233448685MaRDI QIDQ1155902

Anatole Katok

Publication date: 1980

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142762

zbMATH Keywords

loosely BernoulliK-automorphismAnosov diffeomorphism which preserves a smooth positive probability measureflow preserving a smooth positive probability measuresmooth skew product transformationweakly mixing flow

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodic theory (37A99) One-parameter continuous families of measure-preserving transformations (28D10)

Related Items (16)

Bernoulli property for certain skew products over hyperbolic systems ⋮ Mixing properties of generalized \(T,T^{-1}\) transformations ⋮ Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés ⋮ Asymptotically Brownian skew products give non-loosely Bernoulli K- automorphisms ⋮ Flexibility of statistical properties for smooth systems satisfying the central limit theorem ⋮ An uncountable family of pairwise non-Kakutani equivalent smooth diffeomorphisms ⋮ Real-analytic realization of uniform circular systems and some applications ⋮ Bernoulli property of subadditive equilibrium states ⋮ Bernoulli property of equilibrium states for certain partially hyperbolic diffeomorphisms ⋮ On the non-equivalence of the Bernoulli and \(K\) properties in dimension four ⋮ Anatole Katok ⋮ On the Bernoulli property for certain partially hyperbolic diffeomorphisms ⋮ ℤⁿ and ℝⁿ cocycle extensions and complementary algebras ⋮ Statistical properties of chaotic systems ⋮ Limit theorems for partially hyperbolic systems ⋮ Bernoulli diffeomorphisms with n − 1 non-zero exponents

Cites Work

• Unnamed Item
• The Cartesian square of the horocycle flow is not loosely Bernoulli
• New \(K\)-automorphisms and a problem of Kakutani
• Topological transitivity of one class of dynamical systems and flows of frames on manifolds of negative curvature
• PARTIALLY HYPERBOLIC DYNAMICAL SYSTEMS
• MONOTONE EQUIVALENCE IN ERGODIC THEORY
• SOME SMOOTH ERGODIC SYSTEMS
• There are No New Anosov Diffeomorphisms on Tori

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