Chacon's automorphism has minimal self joinings

DOI10.1007/BF02797688zbMath0445.28014MaRDI QIDQ1145242

Laif Swanson, Maurice Rahe, Andrés Del Junco

Publication date: 1980

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

zbMATH Keywords

automorphismorbitsminimal self-joiningsweak-mixinginvariant and ergodic measureoff diagonal measure

Mathematics Subject Classification ID

Measure-preserving transformations (28D05)

Related Items (35)

Infinite measure preserving transformations with Radon MSJ ⋮ Topological isomorphism for rank-1 systems ⋮ Weakly isomorphic transformations that are not isomorphic ⋮ On asymmetry of the future and the past for limit self-joinings ⋮ Bounded rank-1 transformations ⋮ A dynamical system with a \(Z^ 2\) centralizer ⋮ Metrics and entropy for non-compact spaces. Appendix by Daniel J. Rudolph ⋮ Invariant measures for Cartesian powers of Chacon infinite transformation ⋮ Measure-theoretic complexity of ergodic systems ⋮ Joining-rank and the structure of finite rank mixing transformations ⋮ On the correlation of the Moebius function with rank-one systems ⋮ Les transformations de Chacon : combinatoire, structure géométrique, lien avec les systèmes de complexité $2n+1$ ⋮ On the spectrum of \(\alpha \)-rigid maps ⋮ The inverse problem for canonically bounded rank-one transformations ⋮ Mixing and sweeping out ⋮ A criterion for a process to be prime ⋮ Substitutions, tiling dynamical systems and minimal self-joinings ⋮ A canonical structure theorem for finite joining-rank maps ⋮ Around simple dynamical systems. Induced joinings and multiple mixing ⋮ On weak mixing, minimality and weak disjointness of all iterates ⋮ Disjointness of Moebius from Horocycle Flows ⋮ Weak limits of powers of Chacon’s automorphism ⋮ Nearly finite Chacon transformation ⋮ A prime system with many self-joinings ⋮ Weak isomorphism of measure-preserving diffeomorphisms ⋮ The joinings within a class of \({\mathbb{Z}{}}^ 2\)-actions ⋮ Non-reversibility and self-joinings of higher orders for ergodic flows ⋮ Rank-one actions, their \((C, F)\)-models and constructions with bounded parameters ⋮ Joining primeness and disjointness from infinitely divisible systems ⋮ Measure-preserving rank one transformations ⋮ Disjointness between bounded rank-one transformations ⋮ An example of a measure-preserving flow with minimal self-joinings ⋮ Antiautomorphismes involutifs des facteurs de von Neumann injectifs. II ⋮ A family of counterexamples in ergodic theory ⋮ A class of multipliers for \({\mathcal W}^\perp\)

Cites Work

• A simple measure-preserving transformation with trivial centralizer
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Unnamed Item

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