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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Absolutely continuous invariant measures that are maximal


Authors: W. Byers and A. Boyarsky
Journal: Trans. Amer. Math. Soc. 290 (1985), 303-314
MSC: Primary 58F08; Secondary 58F11
MathSciNet review: 787967
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Abstract: Let $ A$ be a certain irreducible $ 0{\text{-}}1$ matrix and let $ \tau $ denote the family of piecewise linear Markov maps on $ [0,1]$ which are consistent with $ A$. The main result of this paper characterizes those maps in $ \tau $ whose (unique) absolutely continuous invariant measure is maximal, and proves that for "most" of the maps that are consistent with $ A$, the absolutely continuous invariant measure is not maximal.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0787967-3
PII: S 0002-9947(1985)0787967-3
Article copyright: © Copyright 1985 American Mathematical Society