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

MathSciNet review:
542879

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Abstract: A class of piecewise 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