Abstract
We present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, omega) via the highest Euler-Lagrange cohomology. It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in Hamilton mechanics. The ordinary canonical equations are included as a special case with a 2-form 1/(n - 1)Homega, where H is the corresponding Hamiltonian.
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