Ergodic properties of skew products with Lasota-Yorke type maps in the base

• Autorzy: Zbigniew S. Kowalski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 106
• Numer: 1
• Strony: 45-57

Daty

wydano

1993

otrzymano

1992-05-13

poprawiono

1993-01-12

poprawiono

1993-05-05

Twórcy

autor

Zbigniew S. Kowalski

• Institute of Mathematics, Wrocław Technical University, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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