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Pis'ma v Zh. Èksper. Teoret. Fiz., 2002, Volume 76, Issue 12, Pages 859–862 (Mi jetpl3007)  

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

MISCELLANEOUS

Fractional extensions of the classical isotropic oscillator and the Kepler problem

V. M. Eleonskii, V. G. Korolev, N. E. Kulagin

State Research Institute of Physical Problems

Abstract: The class of fractional Hamiltonian systems that generalize the classical problem of the two-dimensional (2D) isotropic harmonic oscillator and the Kepler problem is considered. It is shown that, in the 4D space of structural parameters, the 2D isotropic harmonic oscillator can be extended along a line in such a way that the orbits remain closed and oscillations remain isochronous. Likewise, the Kepler problem can be extended along a line in such a way that the orbits remain closed for all finite motions and the third Kepler law remains valid. These curves lie on the 2D surfaces where any dynamical system is characterized by the same rotation number for all finite motions.

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English version:
Journal of Experimental and Theoretical Physics Letters, 2002, 76:12, 728–731

Document Type: Article
PACS: 03.20.+i, 95.10.Ce
Received: 31.10.2002

Citation: V. M. Eleonskii, V. G. Korolev, N. E. Kulagin, “Fractional extensions of the classical isotropic oscillator and the Kepler problem”, Pis'ma v Zh. Èksper. Teoret. Fiz., 76:12 (2002), 859–862; JETP Letters, 76:12 (2002), 728–731

Citation in format AMSBIB
\Bibitem{EleKorKul02}
\by V.~M.~Eleonskii, V.~G.~Korolev, N.~E.~Kulagin
\paper Fractional extensions of the classical isotropic oscillator and the Kepler problem
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2002
\vol 76
\issue 12
\pages 859--862
\mathnet{http://mi.mathnet.ru/jetpl3007}
\transl
\jour JETP Letters
\yr 2002
\vol 76
\issue 12
\pages 728--731
\crossref{https://doi.org/10.1134/1.1556215}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0040075927}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Zaur Z. Alisultanov, Ruslan P. Meilanov, “Teplofizicheskie svoistva kvantovo-statisticheskikh sistem s drobno-stepennym spektrom”, Zhurn. SFU. Ser. Matem. i fiz., 5:3 (2012), 349–358  mathnet
    2. Z. Z. Alisultanov, R. P. Meylanov, “Some features of quantum statistical systems with an energy spectrum of the fractional-power type”, Theoret. and Math. Phys., 171:3 (2012), 769–779  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. Z. Z. Alisultanov, R. P. Meylanov, “Some problems of the theory of quantum statistical systems with an energy spectrum of the fractional-power type”, Theoret. and Math. Phys., 173:1 (2012), 1445–1456  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
  •       Pis'ma v Zhurnal ksperimental'noi i Teoreticheskoi Fiziki
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