A variational principle for volume-preserving dynamics

Abstract

We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields 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.

References in corpus (4)

• Hyperhamiltonian dynamics
• Quaternionic Hamilton equations
• Quaternionic integrable systems
• Maximal degree variational principles

Cited by in corpus (5)

• Resonance Zones and Lobe Volumes for Volume-Preserving Maps
• Canonical transformations for hyperkahler structures and hyperhamiltonian dynamics
• Symmetry and quaternionic integrable systems
• Structure preserving transformations in hyperkahler Euclidean spaces
• Variational principles for involutive systems of vector fields