Geodesic
Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. I. Third-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 2, Tome 236 (2024), pp. 72-88

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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 
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     author = {M. V. Shamolin},
     title = {Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. {I.} {Third-order} systems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {236},
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M. V. Shamolin. Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. I. Third-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 2, Tome 236 (2024), pp. 72-88. http://geodesic.mathdoc.fr/item/INTO_2024_236_a5/