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Bi-Hamiltonian partially integrable systemsстатья
- Авторы: Giachetta G., Mangiarotti L., Sardanashvily G.
- Журнал: ArXiv e-prints
- Номер: math.DS/ 0211463
- Год издания: 2002
- Аннотация: Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact) invariant manifold which makes this dynamical system into a partially integrable Hamiltonian system. This Poisson structure is by no means unique. Bi-Hamiltonian partially integrable systems are described in some detail. As an outcome, we state the conditions of quasi-periodic stability (the KAM theorem) for partially integrable Hamiltonian systems.
- Добавил в систему: Сарданашвили Геннадий Александрович