Displaying similar documents to “Statistical periodicity of deterministic systems”

Support overlapping L 1 contractions and exact non-singular transformations

Michael Lin (2000)

Colloquium Mathematicae

Similarity:

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.

Weakly mixing but not mixing quasi-Markovian processes

Zbigniew Kowalski (2000)

Studia Mathematica

Similarity:

Let (f,α) be the process given by an endomorphism f and by a finite partition α = A i i = 1 s of a Lebesgue space. Let E(f,α) be the class of densities of absolutely continuous invariant measures for skew products with the base (f,α). We say that (f,α) is quasi-Markovian if E ( f , α ) ⊂ g : ⋁ B i i = 1 s s u p p g = ⋃ i = 1 s A i × B i . We show that there exists a quasi-Markovian process which is weakly mixing but not mixing. As a by-product we deduce that the set of all coboundaries which are measurable with respect to the ’chequer-wise’ partition for σ ×...