Geodesic
The topology of integrable systems with incomplete fields
Sbornik. Mathematics, Tome 205 (2014) no. 9, pp. 1264-1278

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Liouville's theorem holds for Hamiltonian systems with complete Hamiltonian fields which possess a complete involutive system of first integrals; such systems are called Liouville-integrable. In this paper integrable systems with incomplete Hamiltonian fields are investigated. It is shown that Liouville's theorem remains valid in the case of a single incomplete field, while if the number of incomplete fields is greater, a certain analogue of the theorem holds. An integrable system on the algebra $\mathfrak{sl}(3)$ is taken as an example. Bibliography: 11 titles.
Keywords: integrable systems, incomplete fields
Mots-clés : Liouville's theorem, Lie algebras. 
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     author = {K. R. Aleshkin},
     title = {The topology of integrable systems with incomplete fields},
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     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_9_a1/}
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K. R. Aleshkin. The topology of integrable systems with incomplete fields. Sbornik. Mathematics, Tome 205 (2014) no. 9, pp. 1264-1278. http://geodesic.mathdoc.fr/item/SM_2014_205_9_a1/