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Models for measure preserving transformations

open access: yesTopology 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
Matthew Foreman
exaly   +3 more sources

On the Approximation of Koopman Spectra for Measure Preserving Transformations [PDF]

open access: yesSIAM Journal on Applied Dynamical Systems, 2019
For the class of continuous, measure-preserving automorphisms on compact metric spaces, a procedure is proposed for constructing a sequence of finite-dimensional approximations to the associated Koopman operator on a Hilbert space. These finite-dimensional approximations are obtained from the so-called "periodic approximation" of the underlying ...
Nithin Govindarajan   +2 more
exaly   +4 more sources
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Conjugates of Infinite Measure Preserving Transformations

Canadian Journal of Mathematics, 1988
In this paper we consider a question concerning the conjugacy class of an arbitrary ergodic automorphism σ of a sigma finite Lebesgue space (X, , μ) (i.e., a is a ju-preserving bimeasurable bijection of (X, , μ). Specifically we proveTHEOREM 1. Let τ, σ be any pair of ergodic automorphisms of an infinite sigma finite Lebesgue space (X, , μ).
Alpern, S., Choksi, J. R., Prasad, V. S.
openaire   +2 more sources

Commuting measure-preserving transformations

Israel Journal of Mathematics, 1972
Let φ1, ... ,φd be commuting measure-preserving transformations, \( \phi ^l \equiv \phi _1^{l_1 } \phi _2^{l_2 } \cdot \cdot \cdot \phi _d^{l_d } ,\Phi = \left\{ {\phi ^l } \right\} \). The Kakutani-Rokhlin tower theorem is proved in a refined form for non-periodic groups Φ, and the Shannon-McMillan theorem is extended to ergodic groups.
Katznelson, Yitzhak, Weiss, Benjamin
openaire   +1 more source

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