Simple systems and their higher order self-joinings

DOI10.1007/BF02801575zbMath0779.28010MaRDI QIDQ1802736

Daniel J. Rudolph, Bernard Host, Shmuel Glasner

Publication date: 29 June 1993

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

simplicitymeasure-preserving transformationjoiningsergodic systemsimple systemabsolutely continuous spectral typeminimal self joiningsRényi mixing

Mathematics Subject Classification ID

Measure-preserving transformations (28D05)

Related Items (20)

Informal research statement ⋮ On the class of multipliers for W^⊥ ⋮ On some generic classes of ergodic measure preserving transformations ⋮ Disjointness, divisibility, and quasi-simplicity of measure-preserving actions ⋮ Even and odd primality of dynamical systems with invariant measure ⋮ Polymorphisms, joinings, and the tensor simplicity of dynamical systems ⋮ Cut-and-stack simple weakly mixing map with countably many prime factors ⋮ Ergodic transformations conjugate to their inverses by involutions ⋮ Substitutions, tiling dynamical systems and minimal self-joinings ⋮ Stochastic intertwinings and multiple mixing of dynamical systems ⋮ Around simple dynamical systems. Induced joinings and multiple mixing ⋮ On simplicity concepts for ergodic actions ⋮ A prime system with many self-joinings ⋮ Self-joinings of commutative actions with invariant measure ⋮ Rank-one actions, their \((C, F)\)-models and constructions with bounded parameters ⋮ Quasifactors of ergodic systems with positive entropy ⋮ On embeddability of automorphisms into measurable flows from the point of view of self-joining properties ⋮ Measure-preserving rank one transformations ⋮ A simple map with no prime factors ⋮ Rokhlin's multiple mixing problem in the class of positive local rank actions

Cites Work

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• An example of a measure preserving map with minimal self-joinings, and applications
• A criterion for a process to be prime
• Mixing of all orders and pairwise independent joinings of systems with singular spectrum
• Ergodic properties where order 4 implies infinite order
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation

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