Invariants of homogeneous dynamical systems of arbitrary odd order with dissipation

Title	Invariants of homogeneous dynamical systems of arbitrary odd order with dissipation
Authors	M. V. Shamolin¹ ¹National Research Mordovia State University
Annotation	New cases of integrable dynamical systems homogeneous in terms of variables of arbitrary odd order are presented, in which a system on a tangent bundle to an even-dimensional manifold can be distinguished. In this case, the force field (the shear generator in the system) is divided into an internal (conservative) and an external one, which has a dissipation of different signs. The external field is introduced using some unimodular transformation and generalizes the previously considered fields. Complete sets of both the first integrals and invariant differential forms are given.
Keywords	invariant of a dynamical system, essential singular points of invariant, system with dissipation, integrability
Citation	Shamolin M. V. ''Invariants of homogeneous dynamical systems of arbitrary odd order with dissipation'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 281-284. Available at: https://conf.svmo.ru/files/2025/papers/paper57.pdf. - Date of access: 30.08.2025.