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Models for measure preserving transformations

Topology and its Applications, 2010
This is an attractive survey of some recent work of the author, Dan Rudolph and Benjamin Weiss on classification problems in ergodic theory from the point of view of set theory. A particular focus is how statements about the complexity or the genericity of a dynamical property (for example, mixing, weak-mixing, zero entropy, and so on) or a dynamically
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Zero Krengel Entropy does not kill Poisson Entropy [PDF]

, 2010
We prove that the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measure-preserving transformation with zero Krengel entropy (the induced ...
De La Rue, Thierry, Janvresse, Élise
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Towers for commuting endomorphisms, and combinatorial applications [PDF]

, 2016
We give an elementary proof of a generalization of Rokhlin's lemma for commuting non-invertible measure-preserving transformations, and we present several combinatorial applications.Comment: 13 pages. Referee's comments incorporated. To appear in Annales
Avila, Artur, Candela, Pablo
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Biinvariant functions on the group of transformations leaving a measure quasiinvariant [PDF]

, 2014
Let $Gms$ be the group of transformations of a Lebesgue space leaving the measure quasiinvariant, let $Ams$ be its subgroup consisting of transformations preserving the measure.
Neretin, Yuri A.
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Invariance of Poisson measures under random transformations [PDF]

, 2011
We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition.
Privault, Nicolas
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On Partially Trace Distance Preserving Maps and Reversible Quantum Channels

Journal of Applied Mathematics, 2013
We give a characterization of trace-preserving and positive linear maps preserving trace distance partially, that is, preservers of trace distance of quantum states or pure states rather than all matrices.
Long Jian, Kan He, Qing Yuan, Fei Wang
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Multiple recurrence for non-commuting transformations along rationally independent polynomials [PDF]

, 2017
We prove a multiple recurrence result for arbitrary measure-preserving transformations along polynomials in two variables of the form $m+p_i(n)$, with rationally independent $p_i$'s with zero constant term. This is in contrast to the single variable case,
Frantzikinakis, Nikos, Zorin-Kranich, Pavel   +1 more
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Approximation Theories for Measure Preserving Transformations [PDF]

Transactions of the American Mathematical Society, 1944
Not ...
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Infinite Dimensional Maximal Torus Revisited

Mathematics
Let Tm be the maximal torus of a set of m×m unitary diagonal matrices. Let T be a collection of all maps that rigidly rotate every circle of latitude of the sphere with a fixed angle.
Mohamed Lemine H. Bouleryah, Akram Ali, Piscoran Laurian-Ioan   +2 more
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Predictability, entropy and information of infinite transformations

, 2009
We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets.
Aaronson, Jon, Park, Kyewon Koh
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