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

This article is cited in 16 scientific papers (total in 16 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.

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

Bibliographic databases:

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, 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
\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.
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 256
\pages 188--205

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    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. V. V. Kozlov, “Dinamika sistem s servosvyazyami. II”, Nelineinaya dinam., 11:3 (2015), 579–611  mathnet
    12. Valery V. Kozlov, “The Dynamics of Systems with Servoconstraints. II”, Regul. Chaotic Dyn., 20:4 (2015), 401–427  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    13. Kozlov V.V., “On the equations of the hydrodynamic type”, Pmm-J. Appl. Math. Mech., 80:3 (2016), 209–214  crossref  mathscinet  isi  scopus
    14. 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
    15. V. V. Kozlov, “Tensor invariants and integration of differential equations”, Russian Math. Surveys, 74:1 (2019), 111–140  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    16. De Leo R., “A Survey on Quasiperiodic Topology”, Advanced Mathematical Methods in Biosciences and Applications, Steam-H Science Technology Engineering Agriculture Mathematics & Health, ed. Berezovskaya F. Toni B., Springer International Publishing Ag, 2019, 53–88  crossref  mathscinet  isi
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