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 Mat. Sb., 2004, Volume 195, Number 12, Pages 95–108 (Mi msb867)

Non-unique inclusion in a flow and vast centralizer of a generic measure-preserving transformation

A. M. Stepin, A. M. Eremenko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The problem of the inclusion in a flow is considered for a measure-preserving transformation. It is shown that if a transformation $T$ has a simple spectrum, then the set of flows including $T$ – provided that it is not empty – consists either of a unique element or of infinitely many spectrally non-equivalent flows.
It is proved that, generically, inclusions in a flow are maximally non-unique in the following sense: the centralizer of a generic transformation contains a subgroup isomorphic to an infinite-dimensional torus. The corresponding proof is based on the so-called dynamical alternative, a topological analogue of Fubini's theorem, a fundamental fact from descriptive set theory about the almost openness of analytic sets, and Dougherty's lemma describing conditions ensuring that the image of a separable metric space is a second-category set.

DOI: https://doi.org/10.4213/sm867

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English version:
Sbornik: Mathematics, 2004, 195:12, 1795–1808

Bibliographic databases:

UDC: 517.987.5+938.5
MSC: 37A05, 37A10

Citation: A. M. Stepin, A. M. Eremenko, “Non-unique inclusion in a flow and vast centralizer of a generic measure-preserving transformation”, Mat. Sb., 195:12 (2004), 95–108; Sb. Math., 195:12 (2004), 1795–1808

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb867
• https://doi.org/10.4213/sm867
• http://mi.mathnet.ru/eng/msb/v195/i12/p95

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Related articles on Google Scholar: Russian articles, English articles

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