Geodesic
Generalized completely integrable systems
Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 1

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Dynamical systems more general than Hamiltonian systems are considered. The role of the Hamiltonian function is played by a $1$-form (not necessarily closed) on a symplectic phase space. A bracket of such forms is introduced and a generalized Liouville theorem on the complete integrability is formulated. This generalization allows us to better understand the meaning of the conditions of the classical theorem on the complete integrability of the Hamilton equations and to reveal the role of tensor invariants.
DOI : 10.2298/TAM250110011K
Classification : 37J35, 70G65
Keywords: symplectic manifold, differential forms, distributions, Hamilton equations, Lie bracket, Poisson bracket, tensor invariants, complete integrability 
Valery V. Kozlov. Generalized completely integrable systems. Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 1 . doi: 10.2298/TAM250110011K
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