%0 Journal Article
%@ 1930-5311
%A Kosloff, Zemer
%A Soo, Terry
%D 2024
%F discovery:10193041
%J Journal of Modern Dynamics
%P 597-634
%T Sinai factors of nonsingular systems: Bernoulli shifts and Anosov flows
%U https://discovery.ucl.ac.uk/id/eprint/10193041/
%V 20
%X We show that a totally dissipative system has all nonsingular systems as  factors, but that this is no longer true when the factor maps are required to  be finitary. In particular, if a nonsingular Bernoulli shift satisfies the  Doeblin condition, and has a limiting marginal distribution p, then it cannot  have, as a finitary factor, an independent and identically distributed (iid)  system of entropy larger than H(p); on the other hand, we show that iid systems  with entropy strictly lower than H(p) can be obtained as finitary factors of  these Bernoulli shifts, extending Keane and Smorodinsky's finitary version of  Sinai's factor theorem to the nonsingular setting. As a consequence of our  results we also obtain that every transitive twice continuously differentiable  Anosov diffeomorphism on a compact manifold, endowed with volume measure, has  iid factors, and if the factor is required to be finitary, then the iid factor  cannot have Kolmogorov-Sinai entropy greater than the measure-theoretic entropy  of a Sinai-Ruelle-Bowen measure associated with the Anosov diffeomorphism.
%Z This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.