On Absolutely Continuous Invariant Measures and Krieger-Type of Markov Subshifts
Dynamical Systems
2022-12-07 v4
Abstract
It is shown that for a non-singular conservative shift on a topologically mixing Markov subshift with Doeblin Condition the only possible absolutely continuous shift-invariant measure is a Markov measure. Moreover, if it is not equivalent to a homogeneous Markov measure then the shift is of Krieger-type . A criterion for equivalence of Markov measures is included.
Keywords
Cite
@article{arxiv.2004.05781,
title = {On Absolutely Continuous Invariant Measures and Krieger-Type of Markov Subshifts},
author = {Nachi Avraham-Re'em},
journal= {arXiv preprint arXiv:2004.05781},
year = {2022}
}
Comments
Incorporating referee's remark and notations as in the published version in Journal d'Analyse Math\'ematique