A topological lens for a measure-preserving system

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dc.creatorGlasner, Eli
dc.creatorLemanczyk, Mariusz
dc.creatorWeiss, Benjamin
dc.date2009-01-09
dc.date.accessioned2026-07-07T12:28:03Z
dc.date.available2026-07-07T12:28:03Z
dc.descriptionWe introduce a functor which associates to every measure preserving system (X,B,μ,T) a topological system (C_2(μ),\tilde{T}) defined on the space of 2-fold couplings of μ, called the topological lens of T. We show that often the topological lens "magnifies" the basic measure dynamical properties of T in terms of the corresponding topological properties of \tilde{T}. Some of our main results are as follows: (i) T is weakly mixing iff \tilde{T} is topologically transitive (iff it is topologically weakly mixing). (ii) T has zero entropy iff \tilde{T} has zero topological entropy, and T has positive entropy iff \tilde{T} has infinite topological entropy. (iii) For T a K-system, the topological lens is a P-system (i.e. it is topologically transitive and the set of periodic points is dense; such systems are also called chaotic in the sense of Devaney).
dc.identifierhttps://arxiv.org/abs/0901.1247
dc.identifierhttp://arxiv.org/abs/0901.1247
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215412
dc.subjectDynamical Systems
dc.subjectFunctional Analysis
dc.subject37A05, 37A35, 37B05, 37B40
dc.titleA topological lens for a measure-preserving system
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