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Support overlapping L 1 contractions and exact non-singular transformations

Michael Lin (2000)

Colloquium Mathematicae

Let T be a positive linear contraction of L 1 of a σ-finite measure space (X,Σ,μ) which overlaps supports. In general, T need not be completely mixing, but it is in the following cases: (i) T is the Frobenius-Perron operator of a non-singular transformation ϕ (in which case complete mixing is equivalent to exactness of ϕ). (ii) T is a Harris recurrent operator. (iii) T is a convolution operator on a compact group. (iv) T is a convolution operator on a LCA group.

Sur la cohomologie dans les schémas de Bernoulli

Thierry de la Rue (2000)

Colloquium Mathematicae

We introduce an invariant of cohomology in Bernoulli shifts, which is used to answer a question about cohomology of Hölder functions with finitary functions whose coding time is integrable. When restricted to the class of Hölder functions, this invariant even provides a criterion of cohomology.

Sur la convergence faible des systèmes dynamiques échantillonnés

Nadine Guillotin-Plantard (2004)

Annales de l’institut Fourier

Soit T α la rotation sur le cercle d’angle irrationnel α , soit ( S k ) k ≥ 0 une marche aléatoire transiente sur ℤ . Soit f ∈ L 2 ( μ ) et H ∈ ] 0 , 1 [ , nous étudions la convergence faible de la suite 1 n H ∑ k = 0 [ n t ] - 1 f ∘ T α S k , n ≥ 1 .

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