Geodesic
Integral invariants of the Hamilton equations
Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 379-393

Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions are found for the existence of integral invariants of Hamiltonian systems. For two-degrees-of-freedom systems these conditions are intimately related to the existence of nontrivial symmetry fields and multivalued integrals. Any integral invariant of a geodesic flow on an analytic surface of genus greater than 1 is shown to be a constant multiple of the Poincaré–Cartan invariant. Poincaré's conjecture that there are no additional integral invariants in the restricted three-body problem is proved. 
@article{MZM_1995_58_3_a6,
     author = {V. V. Kozlov},
     title = {Integral invariants of the {Hamilton} equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {379--393},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a6/}
}
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V. V. Kozlov. Integral invariants of the Hamilton equations. Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 379-393. http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a6/