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

Tom 22 / 1994

Zbigniew Kowalski Applicationes Mathematicae 22 (1994), 155-163 DOI: 10.4064/am-22-2-155-163

Streszczenie

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.

Autorzy

  • Zbigniew Kowalski

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