Nambu dynamics and its noncanonical Hamiltonian representation in many degrees of freedom systems

Abstract Nambu dynamics is a generalized Hamiltonian of more than two variables, whose time evolutions are given by the bracket, generalization canonical Poisson bracket. can always be represented in form noncanonical defining bracket means For evolution to consistent, must satisfy fundamental identity, while Jacobi identity. However, many degrees freedom systems, it well known that identity does not hold. In present paper we show that, even if violated, for corresponding could As an example evaluate these identities semiclassical system coupled oscillators.