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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Exact dynamical systems and the Frobenius-Perron operator
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by A. Lasota and James A. Yorke PDF
Trans. Amer. Math. Soc. 273 (1982), 375-384 Request permission

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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Additional Information
  • © Copyright 1982 American Mathematical Society
  • 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