Generic mixing transformations are rank 1

DOI10.1134/S0001434613010227zbMath1312.37006MaRDI QIDQ1947787

A. I. Bashtanov

Publication date: 26 April 2013

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

weak topologyLebesgue spaceresidualBernoulli shiftconjugacy classmixing transformationsleash topologyrank-one maps

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodicity, mixing, rates of mixing (37A25)

Related Items (6)

Conjugacy classes are dense in the space of mixing \(\mathbb{Z}^d\)-actions ⋮ Group actions: Entropy, mixing, spectra, and generic properties ⋮ Almost sure convergence of the multiple ergodic average for certain weakly mixing systems ⋮ Thouvenot's isomorphism problem for tensor powers of ergodic flows ⋮ Measure-preserving rank one transformations ⋮ Ergodic homoclinic groups, Sidon constructions and Poisson suspensions

Cites Work

• Unnamed Item
• Joining-rank and the structure of finite rank mixing transformations
• The generic automorphism of a Lebesgue space conjugate to a \(G\)-extension for any finite abelian group \(G\).
• The generic transformation can be embedded in a flow.
• Twofold mixing implies threefold mixing for rank one transformations
• A complete metric in the set of mixing transformations
• Complete metric on the set of mixing transformations
• The generic transformation has roots of all orders
• On the genericity of some non-asymptotic dynamical properties
• Non-unique inclusion in a flow and vast centralizer of a generic measure-preserving transformation

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