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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 256, Pages 201–218 (Mi tm462)  
This article is cited in 21 scientific papers (total in 21 papers)

Dynamical Systems with Multivalued Integrals on a Torus

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (236 kB) Citations (21)
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Abstract: Properties of the solutions to differential equations on the torus with a complete set of multivalued first integrals are considered, including the existence of an invariant measure, the averaging principle, and the infiniteness of the number of zeros for integrals of zero-mean functions along trajectories. The behavior of systems with closed trajectories of large period is studied. It is shown that a generic system acquires a limit mixing property as the periods tend to infinity.
Received in August 2006
English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 256, Pages 188–205
DOI: https://doi.org/10.1134/S0081543807010105
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: V. V. Kozlov, “Dynamical Systems with Multivalued Integrals on a Torus”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 201–218; Proc. Steklov Inst. Math., 256 (2007), 188–205
Citation in format AMSBIB
\Bibitem{Koz07}
\by V.~V.~Kozlov
\paper Dynamical Systems with Multivalued Integrals on a Torus
\inbook Dynamical systems and optimization
\bookinfo Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov
\serial Trudy Mat. Inst. Steklova
\yr 2007
\vol 256
\pages 201--218
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm462}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336900}
\zmath{https://zbmath.org/?q=an:1153.37327}
\elib{https://elibrary.ru/item.asp?id=9482615}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 256
\pages 188--205
\crossref{https://doi.org/10.1134/S0081543807010105}
\elib{https://elibrary.ru/item.asp?id=13550596}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248590645}
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    • This publication is cited in the following 21 articles:
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