# Ergodic properties of skew products with Lasota-Yorke type maps in the base

Studia Mathematica (1993)

- Volume: 106, Issue: 1, page 45-57
- ISSN: 0039-3223

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topKowalski, Zbigniew. "Ergodic properties of skew products with Lasota-Yorke type maps in the base." Studia Mathematica 106.1 (1993): 45-57. <http://eudml.org/doc/216002>.

@article{Kowalski1993,

abstract = {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.},

author = {Kowalski, Zbigniew},

journal = {Studia Mathematica},

keywords = {measure-preserving transformations; skew products; Lasota-Yorke type transformation; eigenfunctions; Frobenius-Perron operator; ergodicity; weak mixing; exactness; random perturbations},

language = {eng},

number = {1},

pages = {45-57},

title = {Ergodic properties of skew products with Lasota-Yorke type maps in the base},

url = {http://eudml.org/doc/216002},

volume = {106},

year = {1993},

}

TY - JOUR

AU - Kowalski, Zbigniew

TI - Ergodic properties of skew products with Lasota-Yorke type maps in the base

JO - Studia Mathematica

PY - 1993

VL - 106

IS - 1

SP - 45

EP - 57

AB - 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.

LA - eng

KW - measure-preserving transformations; skew products; Lasota-Yorke type transformation; eigenfunctions; Frobenius-Perron operator; ergodicity; weak mixing; exactness; random perturbations

UR - http://eudml.org/doc/216002

ER -

## References

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