Ergodic Theory via Joinings

By Eli Glasner. 2003

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View Paper: https://www.semanticscholar.org/paper/04c815fcff526aadc771e3c3bac6338041303ade

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In Mathematical Physics

Citations in the corpus

Automorphisms with quasi-discrete spectrum, multiplicative functions and average orthogonality along short intervals (2015, unknown): “[14]) it follows that all non-zero powers of T are isomorphic.”
Local entropy theory (2009, background): “Here is a sample: First recall a question from [31]: Does there exist a minimal c.”
The Haagerup property for locally compact quantum groups (2013, background): “(U) ∈ C 0(G). The origins of the term mixing lie in the theory of dynamical systems – an action of a group Gon a probability space (X,µ) is mixing in the usual dynamical sense (see Deﬁnition 3.4.6 in [Gla]) if and only if the associated Koopman-type representation of Gon L2(X,µ) 0 := L2(X,µ) ⊖C1 is ”
Isomorphic extensions and applications (2015, background): “The reader is referred to Furstenberg’s classical monograph [5], or to [9] for more details and background.”
On Popa's Cocycle Superrigidity Theorem (2006, background): “For references see [2], [13], [1] and references therein.”
A measure-conjugacy invariant for free group actions (2008, background): “H(giα) = nH(α). See, for example, [ Gl03 , prop.”
Stable sets and mean Li–Yorke chaos in positive entropy systems (2012, background): “Take k 1 = 0, then we ﬁnd inductively k 1 , k 2 , ··· such that for each m ≥ 2, one has It is not hard to check that (1)–(4) hold (see for example [26] or [14]).”
Entropy in dynamical systems (2003, methodology): “We refer the reader to the book by Eli Glasner [Glasner, 2003] for an extensive study of joinings in ergodic theory.”
Poisson suspensions and infinite ergodic theory (2008, background): “The Markov operator that describes a relatively independent joining over a σ-finite factor is the conditional expectation operator on this factor (see [7] page 129).”
Recent development of chaos theory in topological dynamics (2015, background): “We refer the reader to [28, 103] for more information on topological entropy, and [31] for a survey of local entropy theory.”
Uniqueness of the measure of maximal entropy for the squarefree flow (2012, methodology): “ny invariant measure η on Ak(p)). In particular, η must be supported on A 1(p). Now suppose that η is any invariant (not necessarily ergodic) measure of maximal entropy on A(p). Then by Thm. 15.12 of [Gla] we have hη(A(p)) = R Y hηy(A(p))dν(y) where η = R Y ηydν(y) is the ergodic decomposition of η,”