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Uspekhi Mat. Nauk, 1970, Volume 25, Issue 2(152), Pages 193–220 (Mi umn5323)  

This article is cited in 11 scientific papers (total in 11 papers)

Metric properties of measure preserving homeomorphisms

A. B. Katok, A. M. Stepin


Abstract: We study “typical” metric (ergodic) properties of measure preserving homeomorphisms of regularly connected cellular polyhedra and of some other spaces. In 1941 Oxtoby and Ulam proved (for a narrower class of spaces) that ergodicity is such a property. Using a modification of their construction and the method of approximating metric automorphisms by periodic ones, we prove in this paper that almost all properties that are “typical' for the metric automorphisms of the Lebesgue spaces are also "typical” for the situation under discussion.

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English version:
Russian Mathematical Surveys, 1970, 25:2, 191–220

Bibliographic databases:

UDC: 513.83
MSC: 28D05, 28D15, 28D20
Received: 09.12.1969

Citation: A. B. Katok, A. M. Stepin, “Metric properties of measure preserving homeomorphisms”, Uspekhi Mat. Nauk, 25:2(152) (1970), 193–220; Russian Math. Surveys, 25:2 (1970), 191–220

Citation in format AMSBIB
\Bibitem{KatSte70}
\by A.~B.~Katok, A.~M.~Stepin
\paper Metric properties of measure preserving homeomorphisms
\jour Uspekhi Mat. Nauk
\yr 1970
\vol 25
\issue 2(152)
\pages 193--220
\mathnet{http://mi.mathnet.ru/umn5323}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=260974}
\zmath{https://zbmath.org/?q=an:0198.55701|0209.27803}
\transl
\jour Russian Math. Surveys
\yr 1970
\vol 25
\issue 2
\pages 191--220
\crossref{https://doi.org/10.1070/RM1970v025n02ABEH003793}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Steven Alpern, “Superhamiltonian graphs”, Journal of Combinatorial Theory, Series B, 25:1 (1978), 62  crossref
    2. A. M. Stepin, “Spectral properties of generic dynamical systems”, Math. USSR-Izv., 29:1 (1987), 159–192  mathnet  crossref  mathscinet  zmath
    3. Steve Alpern, V. S. Prasad, “Dynamics induced on the ends of non-compact manifold”, Ergod Th Dynam Sys, 8:1 (1988)  crossref  mathscinet
    4. G. R. Goodson, V. V. Ryzhikov, “Conjugations, joinings, and direct products of locally rank one dynamical systems”, J Dyn Control Syst, 3:3 (1997), 321  crossref  mathscinet  zmath
    5. V. I. Bogachev, “Measures on topological spaces”, Journal of Mathematical Sciences (New York), 91:4 (1998), 3033  crossref  mathscinet  zmath
    6. Alpern S. Prasad V., “Properties Generic for Lebesgue Space Automorphisms Are Generic for Measure-Preserving Manifold Homeomorphisms”, Ergod. Theory Dyn. Syst., 22:Part 6 (2002), 1587–1620  crossref  isi
    7. J.N. Qiang, S.W. Zhong, “Clarifications on the Integration Path of Transient Energy Function”, IEEE Trans Power Syst, 20:2 (2005), 883  crossref  isi
    8. Bezuglyi S., Kwiatkowski J., Medynets K., “Approximation in Ergodic Theory, Borel, and Cantor Dynamics”, Algebraic and Topological Dynamics, Contemporary Mathematics Series, 385, eds. Kolyada S., Manin Y., Ward T., Amer Mathematical Soc, 2005, 39–64  isi
    9. V. V. Ryzhikov, “Weak limits of powers, simple spectrum of symmetric products, and rank-one mixing constructions”, Sb. Math., 198:5 (2007), 733–754  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. V. V. Ryzhikov, “Spectral multiplicities and asymptotic operator properties of actions with invariant measure”, Sb. Math., 200:12 (2009), 1833–1845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. PIERRE-ANTOINE GUIHÉNEUF, “Dynamical properties of spatial discretizations of a generic homeomorphism”, Ergod. Th. Dynam. Sys, 2014, 1  crossref
  • Успехи математических наук Russian Mathematical Surveys
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