A canonical structure theorem for finite joining-rank maps

DOI10.1007/BF02820465zbMath0735.28010MaRDI QIDQ1177193

Jonathan L. King, Jean-Paul Thouvenot

Publication date: 26 June 1992

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

Lebesgue spacemeasure-preserving mapminimal self-joiningsisomorphism invariant of ergodic mapsjoining-rankfinite-rank mixing mapweak- mixing transformations

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodic theory of linear operators (47A35) Entropy and other invariants (28D20)

Related Items (15)

Bounded rank-1 transformations ⋮ The local rank of an ergodic symmetric power \(T^{\odot n}\) does not exceed \(n! n^{-n}\) ⋮ Disjointness, divisibility, and quasi-simplicity of measure-preserving actions ⋮ Stochastic intertwinings and multiple mixing of dynamical systems ⋮ Around simple dynamical systems. Induced joinings and multiple mixing ⋮ Conjugations, joinings, and direct products of locally rank one dynamical systems ⋮ Disjointness of Moebius from Horocycle Flows ⋮ Rank one and mixing differentiable flows ⋮ On automorphism groups of low complexity subshifts ⋮ Rank, rigidity of factors, and weak closure of measure-preserving \(\mathbb Z^n\)-actions ⋮ Ergodic properties where order 4 implies infinite order ⋮ The almost sure mutual singularity of the spectrum of Ornstein transformations ⋮ Joining primeness and disjointness from infinitely divisible systems ⋮ Rokhlin's multiple mixing problem in the class of positive local rank actions ⋮ On a theorem of Karlin

Cites Work

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• Quasi-factors in ergodic theory
• Joining-rank and the structure of finite rank mixing transformations
• Chacon's automorphism has minimal self joinings
• An example of a measure preserving map with minimal self-joinings, and applications
• Extensions of ergodic group actions
• Ergodic actions with generalized discrete spectrum
• Processes Disjoint from Weak Mixing
• The commutant is the weak closure of the powers, for rank-1 transformations
• An invariant for rigid rank-1 transformations
• Un théorème de disjonction de systèmes dynamiques et une généralisation du théorème ergodique de Wiener—Wintner
• Strict Ergodicity and Transformation of the Torus

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