\(k\)-symplectic Hamiltonian systems (Q700045)

This work is devoted to study Hamiltonian systems in \(k\)-symplectic manifolds which are a generalization of symplectic manifolds, and are applied, for instance, to describe field theories. In this paper, these structures are used for studying the Nambu's statistical mechanics. After defining \(k\)-symplectic Hamiltonian systems and their properties, the integrability of these systems is analyzed in detail. Finally, the Nambu model (in \(\mathbb{R}^{k+1}\)) is treated in this framework. The paper is written in a geometric language.