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, 2025, Volume 238, Pages 69–100
DOI: https://doi.org/10.36535/2782-4438-2025-238-69-100 (Mi into1331) 		 
Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. III. Seventh-order systems

M. V. Shamolin

Lomonosov Moscow State University
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DOI: https://doi.org/10.36535/2782-4438-2025-238-69-100
Abstract: In this paper, we present new examples of integrable dynamical systems of the seventh order that are homogeneous in part of the variables. In these systems, subsystems on the tangent bundles of lower-dimensional manifolds can be distinguished. In the cases considered, the force field is partitioned into an internal (conservative) part and an external part. The external force introduced by a certain unimodular transformation has alternate dissipation; it is a generalization of fields examined earlier. Complete sets of first integrals and invariant differential forms are presented. The first part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 236 (2024), pp. 72–88. The second part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 237 (2024), pp. 49–75.
Keywords: dynamical system, integrability, dissipation, first integral with essential singular points, invariant differential form
English version:
Journal of Mathematical Sciences (New York), 2025, Volume 291, Issue 3, Pages 400–431
DOI: https://doi.org/10.1007/s10958-025-07820-2
Document Type: Article
UDC: 517.9; 531.01
MSC: 34Cxx, 70Cxx
Language: Russian
Citation: M. V. Shamolin, “Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. III. Seventh-order systems”, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 238, VINITI, Moscow, 2025, 69–100; J. Math. Sci. (N. Y.), 291:3 (2025), 400–431
Citation in format AMSBIB
\Bibitem{Sha25}
\by M.~V.~Shamolin
\paper Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. III. Seventh-order systems
\inbook Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2025
\vol 238
\pages 69--100
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1331}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2025
\vol 291
\issue 3
\pages 400--431
\crossref{https://doi.org/10.1007/s10958-025-07820-2}
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