Ergodic properties of skew products with Lasota-Yorke type maps in the base
Volume 106 / 1993
Studia Mathematica 106 (1993), 45-57
DOI: 10.4064/sm-106-1-45-57
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.
