Mathematics – Differential Geometry
Scientific paper
2006-01-26
Mathematics
Differential Geometry
final version
Scientific paper
Using the characterization of last multipliers as solutions of the Liouville's transport equation, new results are given in this approach of ODE by providing several new characterizations, e.g. in terms of Witten and Marsden differentials or adjoint vector field. Applications to Hamiltonian vector fields on Poisson manifolds and vector fields on Riemannian manifolds are presented. In Poisson case, the unimodular bracket considerably simplifies computations while, in the Riemannian framework, a Helmholtz type decomposition yields remarkable examples: one is the quadratic porous medium equation, the second (the autonomous version of the previous) produces harmonic square functions, while the third refers to the gradient of the distance function with respect to a two dimensional rotationally symmetric metric. A final example relates the solutions of Helmholtz (particularly Laplace) equation to provide a last multiplier for a gradient vector field. A connection of our subject with gas dynamics in Riemannian setting is pointed at the end.
No associations
LandOfFree
Last multipliers as autonomous solutions of the Liouville equation of transport does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Last multipliers as autonomous solutions of the Liouville equation of transport, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Last multipliers as autonomous solutions of the Liouville equation of transport will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-171234