Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 145, Pages 86–94 (Mi into282)  
Dissipative Integrable Systems on the Tangent Bundles of $2$- and $3$-Dimensional Spheres

M. V. Shamolin

Lomonosov Moscow State University
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Abstract: In this paper, we prove the explicit integrability of certain classes of dynamical systems on the tangent bundles of $2$- and $3$-dimensional spheres in the case where forces are fields with so-called variable dissipation.
Keywords: dynamical system, dissipation, transcendental first integral, integrability.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-00848-a
This work was partially supported by the Russian Foundation for Basic Research (project No. 15-01-00848-a).
English version:
Journal of Mathematical Sciences, 2020, Volume 245, Issue 4, Pages 498–507
DOI: https://doi.org/10.1007/s10958-020-04706-3
Bibliographic databases:
Document Type: Article
UDC: 517.9; 531.01
MSC: 34Cxx, 37E10, 37N05
Language: Russian
Citation: M. V. Shamolin, “Dissipative Integrable Systems on the Tangent Bundles of $2$- and $3$-Dimensional Spheres”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 145, VINITI, M., 2018, 86–94; Journal of Mathematical Sciences, 245:4 (2020), 498–507
Citation in format AMSBIB
\Bibitem{Sha18}
\by M.~V.~Shamolin
\paper Dissipative Integrable Systems on the Tangent Bundles of $2$- and~$3$-Dimensional Spheres
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 145
\pages 86--94
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into282}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3824391}
\transl
\jour Journal of Mathematical Sciences
\yr 2020
\vol 245
\issue 4
\pages 498--507
\crossref{https://doi.org/10.1007/s10958-020-04706-3}
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