Nachi Avraham-Re'em
Published 2020-04-13Version 1
It is shown that for a non-singular conservative shift on a topologically-mixing Markov subshift with $\textit{Doeblin Condition}$, the only possible absolutely continuous shift-invariant measure is a homogeneous Markov measure. Moreover, if it is not equivalent to a homogeneous Markov measure then the shift is of Krieger-type $\mathrm{III}_1$. A criterion for equivalence of Markov measures is included.
Non-uniform hyperbolicity and existence of absolutely continuous invariant measures
Selections and their Absolutely Continuous Invariant Measures
Absolutely continuous invariant measures for random non-uniformly expanding maps
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