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<https://discovery.ucl.ac.uk/id/eprint/10193041> <http://purl.org/dc/terms/title> "Sinai factors of nonsingular systems: Bernoulli shifts and Anosov flows"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10193041> <http://purl.org/ontology/bibo/abstract> "We show that a totally dissipative system has all nonsingular systems as\r\nfactors, but that this is no longer true when the factor maps are required to\r\nbe finitary. In particular, if a nonsingular Bernoulli shift satisfies the\r\nDoeblin condition, and has a limiting marginal distribution p, then it cannot\r\nhave, as a finitary factor, an independent and identically distributed (iid)\r\nsystem of entropy larger than H(p); on the other hand, we show that iid systems\r\nwith entropy strictly lower than H(p) can be obtained as finitary factors of\r\nthese Bernoulli shifts, extending Keane and Smorodinsky's finitary version of\r\nSinai's factor theorem to the nonsingular setting. As a consequence of our\r\nresults we also obtain that every transitive twice continuously differentiable\r\nAnosov diffeomorphism on a compact manifold, endowed with volume measure, has\r\niid factors, and if the factor is required to be finitary, then the iid factor\r\ncannot have Kolmogorov-Sinai entropy greater than the measure-theoretic entropy\r\nof a Sinai-Ruelle-Bowen measure associated with the Anosov diffeomorphism."^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10193041> <http://purl.org/dc/terms/date> "2024-12" .
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