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Tensor invariants of geodesic, potential and dissipative systems. III. Systems on tangents bundles of four-dimensional manifolds
M. V. Shamolin Lomonosov Moscow State University
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
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
Linking options:
https://www.mathnet.ru/eng/into1238 https://www.mathnet.ru/eng/into/v229/p90
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