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Measure-preserving rank one transformations (Q4985021)

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scientific article; zbMATH DE number 7336241

Language	Label	Description	Also known as
English	Measure-preserving rank one transformations	scientific article; zbMATH DE number 7336241

Statements

scholarly article

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Measure-preserving rank one transformations (English)

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Transactions of the Moscow Mathematical Society

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publication date

21 April 2021

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full work available at URL

https://arxiv.org/abs/2005.00449

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zbMATH Keywords

ergodic action

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rank-one action

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multiple mixing

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weak closure

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self-joining

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spectrum

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MaRDI profile type

MaRDI publication profile

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Generic mixing transformations are rank 1

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APPROXIMATIONS IN ERGODIC THEORY

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Weak closures of ergodic actions

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Special weak limits and simple spectrum of the tensor products of flows

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An automorphism with simple, continuous spectrum not having the group property

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Two nonisomorphic dynamical systems with the same simple continuous spectrum

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Intertwinings of tensor products, and the stochastic centralizer of dynamical systems

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Rokhlin's multiple mixing problem in the class of positive local rank actions

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On the spectral and mixing properties of rank-one constructions in ergodic theory

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Disjointness, divisibility, and quasi-simplicity of measure-preserving actions

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Factors, rank, and embedding of a generic $ \mathbb Z^n$-action in an $ \mathbb R^n$-flow

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Weak limits of powers, simple spectrum of symmetric products, and rank-one mixing constructions

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Bounded ergodic constructions, disjointness, and weak limits of powers

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Ergodic homoclinic groups, Sidon constructions and Poisson suspensions

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On the centralizer of an infinite mixing rank-one transformation

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Thouvenot's isomorphism problem for tensor powers of ergodic flows

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Weakly homoclinic groups of ergodic actions

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Weak closure of infinite actions of rank 1, joinings, and spectrum

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SPECTRAL PROPERTIES OF GENERIC DYNAMICAL SYSTEMS

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Non-unique inclusion in a flow and vast centralizer of a generic measure-preserving transformation

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Complete metric on the set of mixing transformations

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Smorodinsky’s conjecture on rank-one mixing

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The homogeneous spectrum problem in ergodic theory

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Spectral rigidity of group actions: Applications to the case gr⟨𝑡,𝑠;𝑡𝑠=𝑠𝑡²⟩

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Conjecture: In general a mixing transformation is not two-fold mixing

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A Class of Ergodic Transformations Having Simple Spectrum

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On the spectral type of Ornstein's class one transformations

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On the correlation of the Moebius function with rank-one systems

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Weakly Mixing Transformations Which are Not Strongly Mixing

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A prime system with many self-joinings

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Mixing on rank-one transformations

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A survey on spectral multiplicities of ergodic actions

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On spectral disjointness of powers for rank-one transformations and Möbius orthogonality

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The conjugacy problem in ergodic theory

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Simple systems and their higher order self-joinings

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Mixing of all orders and pairwise independent joinings of systems with singular spectrum

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Around King’s rank-one theorems: Flows and ℤⁿ-actions

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Weak limits of powers of Chacon’s automorphism

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Poisson suspensions and SuShis

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Transformations With Discrete Spectrum are Stacking Transformations

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Chacon's automorphism has minimal self joinings

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A simple map with no prime factors

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Twofold mixing implies threefold mixing for rank one transformations

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

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Joining-rank and the structure of finite rank mixing transformations

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Ergodic properties where order 4 implies infinite order

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The generic transformation has roots of all orders

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Rank one transformations with singular spectral type

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On invariant measures

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Disjointness of the convolutionsfor Chacon's automorphism

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An example of a measure preserving map with minimal self-joinings, and applications

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The generic transformation can be embedded in a flow.

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Stochastic intertwinings and multiple mixing of dynamical systems

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Bounded gaps between primes

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1090/MOSC/310

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Sitelinks

Mathematics(1 entry)

mardi Publication:4985021

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