Kowalski, Zbigniew S. Ergodic properties of skew products with Lasota-Yorke type maps in the base. (English) Zbl 0815.28013 Stud. Math. 106, No. 1, 45-57 (1993). Summary: 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 \(T_ i\), \(i= 1,\dots,\max e\), 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. Cited in 1 Document MSC: 28D05 Measure-preserving transformations Keywords:measure-preserving transformations; skew products; Lasota-Yorke type transformation; eigenfunctions; Frobenius-Perron operator; ergodicity; weak mixing; exactness; random perturbations PDFBibTeX XMLCite \textit{Z. S. Kowalski}, Stud. Math. 106, No. 1, 45--57 (1993; Zbl 0815.28013) Full Text: DOI EuDML