Phase Flows and Vector Hamiltonians

TL;DR

This paper generalizes Nambu mechanics by establishing that the Poisson structure in multisymplectic phase spaces is generated by specific k-Hamiltonian vector fields, expanding the theoretical framework of phase space dynamics.

Contribution

It introduces a novel generalization of Nambu mechanics using k-Hamiltonians to induce Poisson structures in multisymplectic phase spaces.

Findings

Poisson structure is induced by k-Hamiltonian vector fields

Generalization of Nambu mechanics to multisymplectic phase spaces

Introduction of k-Hamiltonians for phase space dynamics

Abstract

We present a generalization of the Nambu mechanics on the base of Liouville's theorem. We prove that the Poisson structure of an n-dimensional multisymplectic phase space is induced by (n-1)-Hamiltonian k-vector field seach of which requires introduction of k-Hamiltonians.