Generalization of Nambu's mechanics (Q1230674)

The author introduces a generalized formalism for integrable mechanical systems. The novelty here is that the dimension of phase space may be odd. This generalizes classical Hamiltonian mechanics as well as Nambu mechanics [the author and \textit{A. J. Kálnay}, Int. J. Theor. Phys. 12, 61--67 (1975; Zbl 0338.70013)]. The author shows that the formalism is invariant under all locally invertible transformations (not necessarily symplectic). Also, it is shown that the formalism extends to classical field theory.