Exactness of skew products with expanding fibre maps

Thomas Bogenschütz; Zbigniew Kowalski

Studia Mathematica (1996)

  • Volume: 120, Issue: 2, page 159-168
  • ISSN: 0039-3223

Abstract

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

How to cite

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Bogenschütz, Thomas, and Kowalski, Zbigniew. "Exactness of skew products with expanding fibre maps." Studia Mathematica 120.2 (1996): 159-168. <http://eudml.org/doc/216327>.

@article{Bogenschütz1996,
abstract = {We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.},
author = {Bogenschütz, Thomas, Kowalski, Zbigniew},
journal = {Studia Mathematica},
keywords = {fibre maps; skew products; random dynamical systems; Lebesgue measure},
language = {eng},
number = {2},
pages = {159-168},
title = {Exactness of skew products with expanding fibre maps},
url = {http://eudml.org/doc/216327},
volume = {120},
year = {1996},
}

TY - JOUR
AU - Bogenschütz, Thomas
AU - Kowalski, Zbigniew
TI - Exactness of skew products with expanding fibre maps
JO - Studia Mathematica
PY - 1996
VL - 120
IS - 2
SP - 159
EP - 168
AB - We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.
LA - eng
KW - fibre maps; skew products; random dynamical systems; Lebesgue measure
UR - http://eudml.org/doc/216327
ER -

References

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  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. Zbl0176.00901
  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. Zbl0587.58027
  9. [Roh64] V. A. Rohlin [V. A. Rokhlin], Exact endomorphisms of a Lebesgue space, Amer. Math. Soc. Transl. Ser. 2 39 (1964), 1-36. Zbl0154.15703

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