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Transactions of the American Mathematical Society

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

 
 

 

On a class of transformations which have unique absolutely continuous invariant measures


Authors: Abraham Boyarsky and Manny Scarowsky
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1979-0542879-2
Article copyright: © Copyright 1979 American Mathematical Society

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