Displaying similar documents to “Locally equicontinuous dynamical systems”

BV coboundaries over irrational rotations

Dalibor Volný (1997)

Studia Mathematica

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For every irrational rotation we construct a coboundary which is continuous except at a single point where it has a jump, is nondecreasing, and has zero derivative almost everywhere.

Remarks on the tightness of cocycles

Jon Aaronson, Benjamin Weiss (2000)

Colloquium Mathematicae

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We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.

Large deviations for generic stationary processes

Emmanuel Lesigne, Dalibor Volný (2000)

Colloquium Mathematicae

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Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.

On the mean ergodic theorem for Cesàro bounded operators

Yves Derriennic (2000)

Colloquium Mathematicae

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For a Cesàro bounded operator in a Hilbert space or a reflexive Banach space the mean ergodic theorem does not hold in general. We give an additional geometrical assumption which is sufficient to imply the validity of that theorem. Our result yields the mean ergodic theorem for positive Cesàro bounded operators in L p (1 < p < ∞). We do not use the tauberian theorem of Hardy and Littlewood, which was the main tool of previous authors. Some new examples, interesting for summability...