We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.
Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
[Die84] J. Diestel, Sequences and Series in Banach Spaces, Springer, New York, 1984.
[Kif92] Y. Kifer, Equilibrium states for random expanding transformations, Random Comput. Dynamics 1 (1992), 1-31.
[KK94] K. Khanin and Y. Kifer, Thermodynamic formalism for random transformations and statistical mechanics, preprint, 1994.
[Kre85] U. Krengel, Ergodic Theorems, Walter de Gruyter, Berlin, 1985.
[KS69] K. Krzyżewski and W. Szlenk, On invariant measures for expanding differentiable mappings, Studia Math. 33 (1969), 83-92.
[Las80] A. Lasota, A fixed point theorem and its application in ergodic theory, Tôhoku Math. J. 32 (1980), 567-575.
[LM94] A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer, New York, 1994 (rev. ed. of: Probabilistic Properties of Deterministic Systems, 1985).
[Mor85] T. Morita, Asymptotic behavior of one-dimensional random dynamical systems, J. Math. Soc. Japan 37 (1985), 651-663.
[Roh64] V. A. Rohlin [V. A. Rokhlin], Exact endomorphisms of a Lebesgue space, Amer. Math. Soc. Transl. Ser. 2 39 (1964), 1-36.