The topology of integrable systems with incomplete fields

Journal Article · Tue Sep 30 00:00:00 EDT 2014 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2014V205N09ABEH004417· OSTI ID:22364892

Aleshkin, K R ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

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 sl(3) is taken as an example. Bibliography: 11 titles.

• OSTI ID: 22364892
• Journal Information: Sbornik. Mathematics, Vol. 205, Issue 9; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGEBRA
HAMILTONIANS
INTEGRAL CALCULUS
INTEGRALS
LIOUVILLE THEOREM
MATHEMATICAL SOLUTIONS
SL GROUPS
TOPOLOGY