Invariant differential forms of various dissipation dynamical systems with a finite number of degrees of freedom

Title	Invariant differential forms of various dissipation dynamical systems with a finite number of degrees of freedom
Authors	M. V. Shamolin¹ ¹Lomonosov Moscow State University
Annotation	For the considered class of homogeneous dynamical systems on tangent bundles to smooth finite-dimensional manifolds, complete sets of tensor invariants, i. e. invariant differential forms, are presented. The connection between the presence of these invariants and the full set of the first integrals which necessary for the integration of the considered geodesic, potential, and dissipative dynamical systems is shown. At the same time, the investigated force fields introduce dissipation of different signs into the systems and generalize the previously considered ones.
Keywords	dynamical system with dissipation, integrability, transcendental tensor invariant
Citation	Shamolin M. V. ''Invariant differential forms of various dissipation dynamical systems with a finite number of degrees of freedom'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 262-264. Available at: https://conf.svmo.ru/files/2023/papers/paper42.pdf. - Date of access: 19.05.2024.