Orbit equivalence rigidity of equicontinuous systems
نویسندگان
چکیده
منابع مشابه
Orbit equivalence rigidity
Consider a countable group Γ acting ergodically by measure preserving transformations on a probability space (X,μ), and let RΓ be the corresponding orbit equivalence relation on X. The following rigidity phenomenon is shown: there exist group actions such that the equivalence relation RΓ on X determines the group Γ and the action (X,μ,Γ) uniquely, up to finite groups. The natural action of SLn(...
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We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative curvature geometry. Amongst our applications are (a) measurable Mostow-type rigidity theorems for products of negatively curved groups; (b) prime factorizat...
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We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with finite local complexity the only equicontinuous systems are then shown to be the crystalline ones. On the other hand, within the class without finite local complexity, we exhibit examples of equicontinuous minimal Delone dynamical s...
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This paper is about ow-orbit equivalence, a topological analogue of even Kakutani equivalence. In addition to establishing many basic facts about this relation, we characterize the conjugacies of induced systems that can be extended to a ow-orbit equivalence. We also describe the relationship between ow-orbit equivalence and a distortion function of an orbit equivalence. We show that if the ...
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A new class of dynamical systems is defined, the class of “locally equicontinuous systems” (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in l∞(Z) form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, w...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2016
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms/jdw047