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, 2022, Volume 209, Pages 108–116
DOI: https://doi.org/10.36535/0233-6723-2022-209-108-116
(Mi into1007)
 

This article is cited in 6 scientific papers (total in 6 papers)

Some tensor invariants of geodesic, potential, and dissipative systems on the tangent bundles of two-dimensional manifolds

M. V. Shamolin

Lomonosov Moscow State University
Full-text PDF (214 kB) Citations (6)
References:
Abstract: In this paper, we construct tensor invariants (differential forms) of homogeneous dynamical systems on the tangent bundles of smooth two-dimensional manifolds. We establish the relationship between the presence of such invariants and the existence of complete sets of first integrals, which are necessary for integrating geodesic, potential, and dissipative systems. Due to force fields, systems considered are dissipative; they are generalizations of systems considered earlier.
Keywords: dynamical system, integrability, dissipation, transcendental first integral, invariant differential form.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00016
%\thanks{This work was supported by the Russian Foundation for Basic Research (project No.~19-01-00016).}
Document Type: Article
UDC: 517.9, 531.01
MSC: 34Cxx, 70Cxx
Language: Russian
Citation: M. V. Shamolin, “Some tensor invariants of geodesic, potential, and dissipative systems on the tangent bundles of two-dimensional manifolds”,  Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 209, VINITI, Moscow, 2022, 108–116
Citation in format AMSBIB
\Bibitem{Sha22}
\by M.~V.~Shamolin
\paper Some tensor invariants of geodesic, potential, and dissipative systems on the tangent bundles of two-dimensional manifolds
\inbook  Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 209
\pages 108--116
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1007}
\crossref{https://doi.org/10.36535/0233-6723-2022-209-108-116}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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    References:40
     
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