The topology of integrable systems with incomplete fields
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...
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| Veröffentlicht in: | Sbornik. Mathematics 2014-01, Vol.205 (9), p.1264-1278 |
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| container_title | Sbornik. Mathematics |
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| creator | Aleshkin, K. R. |
| description | 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 is taken as an example. Bibliography: 11 titles. |
| doi_str_mv | 10.1070/SM2014v205n09ABEH004417 |
| format | Article |
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| ispartof | Sbornik. Mathematics, 2014-01, Vol.205 (9), p.1264-1278 |
| issn | 1064-5616 1468-4802 |
| language | eng |
| recordid | cdi_iop_journals_10_1070_SM2014v205n09ABEH004417 |
| source | IOP Publishing Journals; Alma/SFX Local Collection |
| subjects | ALGEBRA Analogue HAMILTONIANS incomplete fields integrable systems INTEGRAL CALCULUS INTEGRALS Lie algebras LIOUVILLE THEOREM Liouville's theorem Mathematical analysis MATHEMATICAL METHODS AND COMPUTING MATHEMATICAL SOLUTIONS SL GROUPS Theorems TOPOLOGY |
| title | The topology of integrable systems with incomplete fields |
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