The commutant is the weak closure of the powers, for rank-1 transformations

DOI10.1017/S0143385700003552zbMath0595.47005OpenAlexW2061575150MaRDI QIDQ3726823

Jonathan L. King

Publication date: 1986

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700003552

zbMATH Keywords

rigidweak isomorphismcommutant semigrouprank-1 transformationsany proper factor of a rank-1 must bebetween two transformations

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodic theory of linear operators (47A35) Groups and semigroups of linear operators (47D03)

Related Items (35)

Topological isomorphism for rank-1 systems ⋮ On asymmetry of the future and the past for limit self-joinings ⋮ Bounded rank-1 transformations ⋮ Extensions of cocycles for hyperfinite actions and applications ⋮ A lower bound on the rank of mixing extensions ⋮ On the work of V. A. Rokhlin in ergodic theory ⋮ Joining-rank and the structure of finite rank mixing transformations ⋮ Generic representations of abelian groups and extreme amenability ⋮ Dynamical properties of minimal Ferenczi subshifts ⋮ Non-rigid rank-one infinite measures on the circle ⋮ On the centralizer of an infinite mixing rank-one transformation ⋮ The conjugacy problem in ergodic theory ⋮ Whirly 3-interval exchange transformations ⋮ Substitutions, tiling dynamical systems and minimal self-joinings ⋮ A canonical structure theorem for finite joining-rank maps ⋮ Conjugations, joinings, and direct products of locally rank one dynamical systems ⋮ Extensions of generic measure-preserving actions ⋮ Polish groups and Baire category methods ⋮ Centralizers of rank-one homeomorphisms ⋮ Subsequence bounded rational ergodicity of rank-one transformations ⋮ For mixing transformations \(rank(T^ k)=k\cdot rank(T)\) ⋮ A prime system with many self-joinings ⋮ Partially bounded transformations have trivial centralizers ⋮ Rank, rigidity of factors, and weak closure of measure-preserving \(\mathbb Z^n\)-actions ⋮ Self-joinings for 3-IETs ⋮ Rank-one ℤ^d actions and directional entropy ⋮ Weak closure of infinite actions of rank 1, joinings, and spectrum ⋮ Unnamed Item ⋮ Measure-preserving rank one transformations ⋮ Rank of Gaussian dynamical systems ⋮ Polyhomomorphisms of locally compact groups ⋮ Disjointness between bounded rank-one transformations ⋮ Unnamed Item ⋮ The centralizer of a rank-one flow ⋮ Stochastic intertwinings and joinings of dynamical systems

Cites Work

• Theory of dynamical systems and general transformation groups with invariant measure
• Prime flows in topological dynamics
• Transformations With Discrete Spectrum are Stacking Transformations
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Commuting Transformations and Mixing

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