# Ergodic properties of skew products withfibre maps of Lasota-Yorke type

Applicationes Mathematicae (1994)

- Volume: 22, Issue: 2, page 155-163
- ISSN: 1233-7234

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topKowalski, Zbigniew. "Ergodic properties of skew products withfibre maps of Lasota-Yorke type." Applicationes Mathematicae 22.2 (1994): 155-163. <http://eudml.org/doc/219088>.

@article{Kowalski1994,

abstract = {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.},

author = {Kowalski, Zbigniew},

journal = {Applicationes Mathematicae},

keywords = {Frobenius-Perron operator; invariant measure; motion of cogged bits; fibre maps; skew product transformation; Lasota-Yorke type maps; ergodic properties},

language = {eng},

number = {2},

pages = {155-163},

title = {Ergodic properties of skew products withfibre maps of Lasota-Yorke type},

url = {http://eudml.org/doc/219088},

volume = {22},

year = {1994},

}

TY - JOUR

AU - Kowalski, Zbigniew

TI - Ergodic properties of skew products withfibre maps of Lasota-Yorke type

JO - Applicationes Mathematicae

PY - 1994

VL - 22

IS - 2

SP - 155

EP - 163

AB - 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.

LA - eng

KW - Frobenius-Perron operator; invariant measure; motion of cogged bits; fibre maps; skew product transformation; Lasota-Yorke type maps; ergodic properties

UR - http://eudml.org/doc/219088

ER -

## References

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- [6] Z. S. Kowalski, Ergodic properties of skew products with Lasota-Yorke type maps in the base, ibid. 106 (1993), 45-57. Zbl0815.28013
- [7] A. Lasota and P. Rusek, An application of ergodic theory to the determination of the efficiency of cogged drilling bits, Archiwum Górnictwa 3 (1974), 281-295 (in Polish).
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