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1
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Weakly mixing but not mixing quasi-Markovian processes

100%
Kowalski Z. S.
Studia Mathematica
|
2000
|
tom 142
|
nr 3
235-244
EN
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 $E(f,α) ⊂ { g: ⋁_{{B_i}_{i=1}^s} supp g = ⋃ _{i=1}^{s} A_{i} × B_i}$. 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 × S, where σ is a Bernoulli shift and S is a weakly mixing automorphism, consists of constants.
2
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Ergodic properties of skew products with Lasota-Yorke type maps in the base

100%
Kowalski Z. S.
Studia Mathematica
|
1993
|
tom 106
|
nr 1
45-57
EN
We consider skew products $T(x,y) = (f(x),T_{e(x)} y)$ preserving a measure which is absolutely continuous with respect to the product measure. Here f is a 1-sided Markov shift with a finite set of states or a Lasota-Yorke type transformation and $T_i$, i = 1,..., max e, are nonsingular transformations of some probability space. We obtain the description of the set of eigenfunctions of the Frobenius-Perron operator for T and consequently we get the conditions ensuring the ergodicity, weak mixing and exactness of T. We apply these results to random perturbations.
3
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Ergodic properties of skew products withfibre maps of Lasota-Yorke type

100%
Kowalski Z. S.
Applicationes Mathematicae
|
1993-1995
|
tom 22
|
nr 2
155-163
EN
We consider the skew product transformation T(x,y)= (f(x), $T_{e(x)}$) where f is an endomorphism of a Lebesgue space (X,A,p), e : X → S and ${T_s}_{s \in S}$ is a family of Lasota-Yorke type maps of the unit interval into itself. We obtain conditions under which the ergodic properties of f imply the same properties for T. Consequently, we get the asymptotical stability of random perturbations of a single Lasota-Yorke type map. We apply this to some probabilistic model of the motion of cogged bits in the rotary drilling of hard rock with high rotational speed.
4
Content available remote

Exactness of skew products with expanding fibre maps

64%
Bogenschütz T., Kowalski Z. S.
Studia Mathematica
|
1996
|
tom 120
|
nr 2
159-168
EN
We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.
5
Content available remote

Stationary perturbations based on Bernoulli processes

38%
Kowalski Z. S.
Studia Mathematica
|
1990
|
tom 97
|
nr 1
53-57
6
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Finite generators of ergodic endomorphisms

38%
Kowalski Z. S.
Colloquium Mathematicum
|
1984-1985
|
tom 49
|
nr 1
87-89
7
Content available remote

Minimal generators for ergodic endomorphisms

38%
Kowalski Z. S.
Studia Mathematica
|
1988
|
tom 91
|
nr 2
85-88
8
Content available remote

A generalized skew product

26%
Kowalski Z. S.
Studia Mathematica
|
1987
|
tom 87
|
nr 3
215-222
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