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, 2024, Volume 236, Pages 72–88
DOI: https://doi.org/10.36535/2782-4438-2024-236-72-88
(Mi into1319)
 

Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. I. Third-order systems

M. V. Shamolin

Lomonosov Moscow State University
References:
Abstract: In this paper, we present new examples of integrable dynamical systems of the third order that are homogeneous in part of the variables. In these systems, subsystems on the tangent bundles of two-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.
Keywords: dynamical system, integrability, dissipation, first integral with essential singular points, invariant differential form
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. I. Third-order systems”, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 236, VINITI, Moscow, 2024, 72–88
Citation in format AMSBIB
\Bibitem{Sha24}
\by M.~V.~Shamolin
\paper Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. I. Third-order systems
\inbook Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2024
\vol 236
\pages 72--88
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1319}
\crossref{https://doi.org/10.36535/2782-4438-2024-236-72-88}
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