Geodesic
Ergodic properties of skew products with Lasota-Yorke type maps in the base
Studia Mathematica, Tome 106 (1993) no. 1, pp. 45-57

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DOI

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. 
Zbigniew S. Kowalski. Ergodic properties of skew products with Lasota-Yorke type maps in the base. Studia Mathematica, Tome 106 (1993) no. 1, pp. 45-57. doi: 10.4064/sm-106-1-45-57
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     title = {Ergodic properties of skew products with {Lasota-Yorke} type maps in the base},
     journal = {Studia Mathematica},
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     year = {1993},
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     language = {en},
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