Geodesic
The Liouville Equation as a Hamiltonian System
Matematičeskie zametki, Tome 108 (2020) no. 3, pp. 360-365

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Smooth dynamical systems on closed manifolds with invariant measure are considered. The evolution of the density of a nonstationary invariant measure is described by the well-known Liouville equation. For ergodic dynamical systems, the Liouville equation is expressed in Hamiltonian form. An infinite collection of quadratic invariants that are pairwise in involution with respect to the Poisson bracket generated by the Hamiltonian structure is indicated.
Mots-clés : Liouville equation
Keywords: Hamiltonian systems, integrability. 
@article{MZM_2020_108_3_a2,
     author = {V. V. Kozlov},
     title = {The {Liouville} {Equation} as a {Hamiltonian} {System}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {360--365},
     publisher = {mathdoc},
     volume = {108},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_3_a2/}
}
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V. V. Kozlov. The Liouville Equation as a Hamiltonian System. Matematičeskie zametki, Tome 108 (2020) no. 3, pp. 360-365. http://geodesic.mathdoc.fr/item/MZM_2020_108_3_a2/