The Generalized Liouville's Theorems via Euler-Lagrange Cohomology Groups on Symplectic Manifold

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dc.creatorGuo, Han-Ying
dc.creatorPan, Jianzhong
dc.creatorZhou, Bin
dc.date2004-08-22
dc.date.accessioned2026-07-07T04:31:24Z
dc.date.available2026-07-07T04:31:24Z
dc.descriptionBased on the Euler-Lagrange cohomology groups $H_{EL}^{(2k-1)}({\cal M}^{2n}) (1 \leqslant k\leqslant n)$ on symplectic manifold $({\cal M}^{2n}, ω)$, 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.
dc.description27 pages, no figure, revtex4
dc.identifierhttps://arxiv.org/abs/math-ph/0408034
dc.identifierhttp://arxiv.org/abs/math-ph/0408034
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57802
dc.subjectMathematical Physics
dc.titleThe Generalized Liouville's Theorems via Euler-Lagrange Cohomology Groups on Symplectic Manifold
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