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Some Results on Bundle Systems for a Countable Discrete Amenable Group Action
We consider the style number, independence number and entropy for a frame bundle dynamical system. The base system of which is a countable discrete...
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A decomposition theorem for unitary group representations on Kaplansky–Hilbert modules and the Furstenberg–Zimmer structure theorem
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky–Hilbert modules over Stone algebras is...
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Relative weak mixing is generic
A classical result of Halmos asserts that among measure preserving transformations the weak mixing property is generic. We extend Halmos’ result to...
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Complete metric on mixing actions of general groups
In this paper the metric on the set of mixing actions of a countable infinite group is introduced so that the corresponding space is complete and...
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One-cohomology and the uniqueness of the group measure space decomposition of a II1 factor
We provide a unified and self-contained treatment of several of the recent uniqueness theorems for the group measure space decomposition of a II 1 ...
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Approximate transitivity property and Lebesgue spectrum
Exploiting a spectral criterion for a system not to be AT we give some new examples of zero entropy systems without the AT property. Our examples...
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Entropy Theory for Cross-Sections
We define the notion of entropy for a cross-section of an action of continuous amenable group, and relate it to the entropy of the ambient action. As...
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A Breiman Type Theorem for Gibbs Measures
For a translation invariant Gibbs measure on a suitable translation invariant configuration set X ⊂ S G , where G is an amenable group and S is a...
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(C, F)-Actions in Ergodic Theory
This is a survey of a recent progress related to the (C, F)-construction of funny rank-one actions for locally compact groups. We exhibit a variety...
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On the dynamics of generic non-Abelian free actions
We investigate some global generic properties of the dynamics associated to non-Abelian free actions in certain special cases. The main properties...
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Asymptotique des nombres de Betti, invariants $l^2$ et laminations
Let K be a finite simplicial complex. We are interested in the asymptotic behavior of the Betti numbers of a sequence of finite sheeted covers of...
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Approximation of the effective conductivity of ergodic media by periodization
This paper is concerned with the approximation of the effective conductivity σ( A , μ) associated to an elliptic operator ∇ xA ( x ,η)∇ ...
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Entropy Theory from the Orbital Point of View
Inspired by [17], we develop an orbital approach to the entropy theory for actions of countable amenable groups. This is applied to extend – with...
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Fitting ideals for finitely presented algebraic dynamical systems
We consider a class of algebraic dynamical systems introduced by Kitchens and Schmidt. Under a weak finiteness condition — the Descending Chain...