The Generalized Liouville's Theorems via EulerLagrange Cohomology Groups on Symplectic Manifold
Abstract
Based on the EulerLagrange cohomology groups $H_{EL}^{(2k1)}({\cal M}^{2n}) (1 \leqslant k\leqslant n)$ on symplectic manifold $({\cal M}^{2n}, \omega)$, their properties and a kind of classification of vector fields on the manifold, we generalize Liouville's theorem in classical mechanics to two sequences, the symplectic(like) and the Hamiltonian(like) Liouville's theorems. This also generalizes Noether's theorem, since the sequence of symplectic(like) Liouville's theorems link to the cohomology directly.
 Publication:

arXiv eprints
 Pub Date:
 August 2004
 arXiv:
 arXiv:mathph/0408034
 Bibcode:
 2004math.ph...8034G
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 27 pages, no figure, revtex4