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

Vilasi, Gaetano

J. Geom. Symmetry Phys. 16, 77-91 (2009).

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.

Reviewer: Vladislav Nikolaevich Dumachev (Voronezh)

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 \((n \ge 3)\)

Keywords:

multi-Hamiltonians systems; Nambu’s dynamics; \(n\)-Lie algebras