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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 5, Pages 1010–1032 (Mi izv1329)  

This article is cited in 3 scientific papers (total in 3 papers)

On oscillatory motions in a certain dynamical system

L. D. Pustyl'nikov


Abstract: A rigorous mathematical justification is given for the possibility of unbounded growth of the energy of a relativistic charged particle in a constant magnetic field and a periodic electric field. It is proved that there is an open subset of initial data with infinite Lebesgue measure in the five-dimensional extended phase space for which the energy of the particle tends to infinity.
Bibliography: 11 titles.

Full text: PDF file (2108 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:2, 325–347

Bibliographic databases:

UDC: 517.93+539.076
MSC: Primary 34C35, 78A35, 81M05; Secondary 70G25, 70G35, 70J25
Received: 12.11.1985

Citation: L. D. Pustyl'nikov, “On oscillatory motions in a certain dynamical system”, Izv. Akad. Nauk SSSR Ser. Mat., 51:5 (1987), 1010–1032; Math. USSR-Izv., 31:2 (1988), 325–347

Citation in format AMSBIB
\Bibitem{Pus87}
\by L.~D.~Pustyl'nikov
\paper On~oscillatory motions in a~certain dynamical system
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 5
\pages 1010--1032
\mathnet{http://mi.mathnet.ru/izv1329}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=925092}
\zmath{https://zbmath.org/?q=an:0677.34043|0661.34040}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 2
\pages 325--347
\crossref{https://doi.org/10.1070/IM1988v031n02ABEH001077}


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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. L. D. Pustyl'nikov, “Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism”, Russian Math. Surveys, 50:1 (1995), 145–189  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. L. D. Pustyl'nikov, “Infinite-dimensional non-linear ordinary differential equations and the KAM theory”, Russian Math. Surveys, 52:3 (1997), 551–604  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. T. Krüger, L. D. Pustyl'nikov, S. Troubetzkoy, “The nonautonomous function-theoretic center problem”, Bol Soc Bras Mat, 30:1 (1999), 1  crossref  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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