English

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 III1\mathrm{III}_1. 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