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Nambu dynamics, \(n\)-Lie algebras and integrability. (English) Zbl 1196.37110

The generalization of a bracket Poisson on a case several Hamiltonians is offered. The connection of this theory with Nambu’s dynamics and analogy to brackets of \(n\)-Lie algebras is shown. As an example the system of spin particles is considered.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
22E70 Applications of Lie groups to the sciences; explicit representations
17A42 Other \(n\)-ary compositions \((n \ge 3)\)
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