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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Exact dynamical systems and the Frobenius-Perron operator


Authors: A. Lasota and James A. Yorke
Journal: Trans. Amer. Math. Soc. 273 (1982), 375-384
MSC: Primary 28D05; Secondary 58F20
DOI: https://doi.org/10.1090/S0002-9947-1982-0664049-X
MathSciNet review: 664049
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Abstract: Conditions are investigated which guarantee exactness for measurable maps on measure spaces. The main application is to certain piecewise continuous maps $ T$ on $ [0,1]$ for which $ T'(0) > 1$. We assume $ [0,1]$ can be broken into intervals on which $ T$ is continuous and convex and at the left end of these intervals $ T = 0$ and $ dt/dx > 0$. Such maps have an invariant absolutely continuous density which is exact.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0664049-X
Article copyright: © Copyright 1982 American Mathematical Society

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