Geodesic
Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. II. Fifth-order systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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 3, Tome 237 (2024), pp. 49-75

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In this paper, we present new examples of integrable dynamical systems of the fifth 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.
Keywords: dynamical system, integrability, dissipation, first integral with essential singular points, invariant differential form 
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     title = {Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. {II.} {Fifth-order} systems},
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M. V. Shamolin. Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. II. Fifth-order systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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 3, Tome 237 (2024), pp. 49-75. http://geodesic.mathdoc.fr/item/INTO_2024_237_a4/