Generalized Nambu dynamics and vectorial Hamiltonians

TL;DR

This paper extends Nambu mechanics using Liouville theorem, demonstrating that Poisson manifolds in multi-symplectic phase space are generated by multiple Hamiltonian vector fields, each associated with multiple Hamiltonians.

Contribution

It introduces a generalized framework for Nambu dynamics based on multi-symplectic geometry and Hamiltonian k-vector fields, expanding the theoretical foundation of multi-Hamiltonian systems.

Findings

Poisson manifolds are generated by (n-1) Hamiltonian k-vector fields

Each k-vector field requires k Hamiltonians

The generalization is based on Liouville theorem

Abstract

On the basis of Liouville theorem the generalization of the Nambu mechanics is considered. Is shown, that Poisson manifolds of n-dimensional multi-symplectic phase space have inducting by (n-1) Hamiltonian k-vector fields, each of which requires of (k)-hamiltonians.