RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Tr. Mat. Inst. Steklova, 2007, Volume 256, Pages 201–218 (Mi tm462)  

This article is cited in 14 scientific papers (total in 14 papers)

Dynamical Systems with Multivalued Integrals on a Torus

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences

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.

Full text: PDF file (236 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 256, 188–205

Bibliographic databases:

Document Type: Article
UDC: 519.21
Received in August 2006

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, Tr. 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 Tr. 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://www.ams.org/mathscinet-getitem?mr=2336900}
\zmath{https://zbmath.org/?q=an:1153.37327}
\elib{http://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{http://elibrary.ru/item.asp?id=13550596}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248590645}


Linking options:
  • http://mi.mathnet.ru/eng/tm462
  • http://mi.mathnet.ru/eng/tm/v256/p201

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Kozlov V.V., “Ob invariantnykh mnogoobraziyakh uravnenii gamiltona”, Prikladnaya matematika i mekhanika, 76:4 (2012), 526–539  mathscinet  elib
    2. V. V. Kozlov, “On Bohl's Argument Theorem”, Math. Notes, 93:1 (2013), 83–89  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Problema dreifa i vozvraschaemosti pri kachenii shara Chaplygina”, Nelineinaya dinam., 9:4 (2013), 721–754  mathnet
    4. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “The Problem of Drift and Recurrence for the Rolling Chaplygin Ball”, Regul. Chaotic Dyn., 18:6 (2013), 832–859  mathnet  crossref  mathscinet  zmath
    5. V. V. Kozlov, “Liouville's equation as a Schrödinger equation”, Izv. Math., 78:4 (2014), 744–757  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Bizyaev I.A., “Nonintegrability and Obstructions To the Hamiltonianization of a Nonholonomic Chaplygin TOP”, Dokl. Math., 90:2 (2014), 631–634  crossref  mathscinet  zmath  isi  elib  scopus
    7. Dragovic V., Radnovic M., “Pseudo-Integrable Billiards and Arithmetic Dynamics”, J. Mod. Dyn., 8:1 (2014), 109–132  crossref  mathscinet  zmath  isi  elib  scopus
    8. V. I. Dragović, M. Radnović, “Pseudo-integrable billiards and double reflection nets”, Russian Math. Surveys, 70:1 (2015), 1–31  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. I. A. Bizyaev, V. V. Kozlov, “Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method”, Sb. Math., 206:12 (2015), 1682–1706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. A. Yu. Anikin, J. Brüning, S. Yu. Dobrokhotov, “Averaging and trajectories of a Hamiltonian system appearing in graphene placed in a strong magnetic field and a periodic potential”, J. Math. Sci., 223:6 (2017), 656–666  mathnet  crossref  mathscinet  elib
    11. Valery V. Kozlov, “The Dynamics of Systems with Servoconstraints. II”, Regul. Chaotic Dyn., 20:4 (2015), 401–427  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    12. Kozlov V.V., “On the equations of the hydrodynamic type”, Pmm-J. Appl. Math. Mech., 80:3 (2016), 209–214  crossref  mathscinet  isi  scopus
    13. Karakhanyan A.L., Shahgholian H., “On a Conjecture of de Giorgi Related to Homogenization”, Ann. Mat. Pura Appl., 196:6 (2017), 2167–2183  crossref  mathscinet  zmath  isi  scopus
    14. V. V. Kozlov, “Tensor invariants and integration of differential equations”, Russian Math. Surveys, 74:1 (2019), 111–140  mathnet  crossref  crossref  adsnasa  isi  elib
  •    . . .  Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:428
    Full text:87
    References:59

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019