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, 2023, Volume 229, Pages 90–119
DOI: https://doi.org/10.36535/0233-6723-2023-229-90-119
(Mi into1238)
 

Tensor invariants of geodesic, potential and dissipative systems. III. Systems on tangents bundles of four-dimensional manifolds

M. V. Shamolin

Lomonosov Moscow State University
References:
Abstract: In this paper, we present tensor invariants (first integrals and differential forms) for dynamical systems on the tangent bundles of smooth $n$-dimensional manifolds separately for $n=1$, $n=2$, $n=3$, $n=4$, and for any finite $n$. We demonstrate the connection between the existence of these invariants and the presence of a full set of first integrals that are necessary for integrating geodesic, potential, and dissipative systems. The force fields acting in systems considered make them dissipative (with alternating dissipation).
The first part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 227 (2023), pp. 100–128.
The second part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 228 (2023), pp. 92–118.
Keywords: dynamical system, integrability, dissipation, transcendental first integral, invariant differential form
Funding agency Grant number
Lomonosov Moscow State University 23-Ш05-07
This work was supported by the Program of Development of the Moscow State University (project No 23-Sh05-07).
Document Type: Article
UDC: 517.9; 531.01
MSC: 34Cxx, 70Cxx
Language: Russian
Citation: M. V. Shamolin, “Tensor invariants of geodesic, potential and dissipative systems. III. Systems on tangents bundles of four-dimensional manifolds”, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 229, VINITI, Moscow, 2023, 90–119
Citation in format AMSBIB
\Bibitem{Sha23}
\by M.~V.~Shamolin
\paper Tensor invariants of geodesic, potential and dissipative systems. III. Systems on tangents bundles of four-dimensional manifolds
\inbook Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 229
\pages 90--119
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1238}
\crossref{https://doi.org/10.36535/0233-6723-2023-229-90-119}
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