On the local Hamiltonian structure of vector fields

Abstract

We derive a canonical form for smooth vector fields on ${\Re }^{n+1}$. We use this to demonstrate the local multi-Hamiltonian nature of the corresponding flows. Associated with the canonical form is an inhomogenious linear PDE whose solutions provide conserved measures. These can be used to construct the local Hamiltonians.

Standard LaTeX, 8 pages, no macros. Appeared in Mod. Phys. Lett. A, Vol.9 No.15 (1994) 1399-1405