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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Invariant densities for random maps of the interval


Author: S. Pelikan
Journal: Trans. Amer. Math. Soc. 281 (1984), 813-825
MSC: Primary 58F11; Secondary 28D05, 58F13
MathSciNet review: 722776
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Abstract: A random map is a discrete time process in which one of a number of functions is selected at random and applied. Here we study random maps of $ [0,1]$ which represent dynamical systems on the square $ [0,1] \times [0,1]$. Sufficient conditions for a random map to have an absolutely continuous invariant measure are given, and the number of ergodic components of a random map is discussed.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0722776-1
PII: S 0002-9947(1984)0722776-1
Article copyright: © Copyright 1984 American Mathematical Society