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ArticleOriginal scientific text

Title

Exactness of skew products with expanding fibre maps

Authors 1, 2

Affiliations

  1. Fachbereich 6 Mathematik, Universität Gesamthochschule Essen, Postfach 103 764, D-45117 Essen, Federal Republic of Germany
  2. Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Abstract

We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.

Bibliography

  1. [Die84] J. Diestel, Sequences and Series in Banach Spaces, Springer, New York, 1984.
  2. [Kif92] Y. Kifer, Equilibrium states for random expanding transformations, Random Comput. Dynamics 1 (1992), 1-31.
  3. [KK94] K. Khanin and Y. Kifer, Thermodynamic formalism for random transformations and statistical mechanics, preprint, 1994.
  4. [Kre85] U. Krengel, Ergodic Theorems, Walter de Gruyter, Berlin, 1985.
  5. [KS69] K. Krzyżewski and W. Szlenk, On invariant measures for expanding differentiable mappings, Studia Math. 33 (1969), 83-92.
  6. [Las80] A. Lasota, A fixed point theorem and its application in ergodic theory, Tôhoku Math. J. 32 (1980), 567-575.
  7. [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).
  8. [Mor85] T. Morita, Asymptotic behavior of one-dimensional random dynamical systems, J. Math. Soc. Japan 37 (1985), 651-663.
  9. [Roh64] V. A. Rohlin [V. A. Rokhlin], Exact endomorphisms of a Lebesgue space, Amer. Math. Soc. Transl. Ser. 2 39 (1964), 1-36.
Studia Mathematica
1996/120/2
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Pages:
159-168
Main language of publication
English
Received
1995-09-13
Accepted
1996-05-06
Published
1996
Exact and natural sciences