Absolutely continuous invariant measures that are maximal

Byers, W.; Boyarsky, A.

doi:10.1090/S0002-9947-1985-0787967-3

Absolutely continuous invariant measures that are maximal
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Trans. Amer. Math. Soc. 290 (1985), 303-314 Request permission

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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