On some generic classes of ergodic measure preserving transformations

DOI10.1090/mosc/312zbMath1498.37005arXiv2009.06901OpenAlexW3085745556WikidataQ114094282 ScholiaQ114094282MaRDI QIDQ5082248

Benjamin Weiss, Shmuel Glasner, Jean-Paul Thouvenot

Publication date: 16 June 2022

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.06901

zbMATH Keywords

loosely Bernoulli systemsBernoulli systemsK-systemsrelative weak mixingcomeager propertiesprime dynamical systems

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Ergodicity, mixing, rates of mixing (37A25) Symbolic dynamics (37B10) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items

Compact families and typical entropy invariants of measure-preserving actions ⋮ An ergodic system is dominant exactly when it has positive entropy ⋮ Zero entropy actions of amenable groups are not dominant

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generic representations of abelian groups and extreme amenability
• Extensions of generic measure-preserving actions
• Classifying the isometric extensions of a Bernoulli shift
• Disjointness, divisibility, and quasi-simplicity of measure-preserving actions
• An example of a measure preserving map with minimal self-joinings, and applications
• A criterion for a process to be prime
• Mixing properties of a class of skew-products
• On the stability of the weak Pinsker property
• A simple map with no prime factors
• The generic automorphism of a Lebesgue space conjugate to a \(G\)-extension for any finite abelian group \(G\).
• Measure concentration and the weak Pinsker property
• Relative weak mixing is generic
• Simple systems and their higher order self-joinings
• Ergodic properties where order 4 implies infinite order
• The generic transformation can be embedded in a flow.
• Residual behavior of induced maps
• Around simple dynamical systems. Induced joinings and multiple mixing
• A prime system with many self-joinings
• On simplicity concepts for ergodic actions
• Skew products of Bernoulli shifts with rotations
• A K-automorphism with no square root and Pinsker's conjecture
• ℤⁿ and ℝⁿ cocycle extensions and complementary algebras
• A topological version of a theorem of Veech and almost simple flows
• Factors, rank, and embedding of a generic $ \mathbb Z^n$-action in an $ \mathbb R^n$-flow
• k-fold mixing lifts to weakly mixing isometric extensions
• SPECTRAL PROPERTIES OF GENERIC DYNAMICAL SYSTEMS
• A weakly mixing upside-down tower of isometric extensions
• A typical dynamical system is not simple or semisimple
• The generic transformation has roots of all orders
• Equivalence of measure preserving transformations
• On the genericity of some non-asymptotic dynamical properties
• Closed subgroups generated by generic measure automorphisms
• Generic properties of extensions
• Embedding lattice actions in flows with multidimensional time
• APPROXIMATIONS IN ERGODIC THEORY
• Ergodic Properties of Affine Transformations and Flows on Nilmanifolds
• Point-Distal Flows
• Non-unique inclusion in a flow and vast centralizer of a generic measure-preserving transformation