We provide a variational description of any Liouville, i.e. volume preserving, autonomous vector field on a smooth manifold. This is obtained via a "maximal degree" variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit formulae.
A variational principle for volume-preserving dynamics / G. Gaeta, P. Morando. - In: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS. - ISSN 1402-9251. - 10:4(2003), pp. 539-554. [10.2991/jnmp.2003.10.4.7]
A variational principle for volume-preserving dynamics
G. GaetaPrimo
;P. MorandoUltimo
2003
Abstract
We provide a variational description of any Liouville, i.e. volume preserving, autonomous vector field on a smooth manifold. This is obtained via a "maximal degree" variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit formulae.
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