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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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On a class of transformations which have unique absolutely continuous invariant measures
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by Abraham Boyarsky and Manny Scarowsky PDF
Trans. Amer. Math. Soc. 255 (1979), 243-262 Request permission

Abstract:

A class of piecewise ${C^2}$ transformations from an interval into itself with slopes greater than 1 in absolute value, and having the property that it takes partition points into partition points is shown to have unique absolutely continuous invariant measures. For this class of functions, a central limit theorem holds for all real measurable functions. For the subclass of piecewise linear transformations having a fixed point, it is shown that the unique absolutely continuous invariant measures are piecewise constant.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 255 (1979), 243-262
  • MSC: Primary 28D05; Secondary 60F05
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0542879-2
  • MathSciNet review: 542879