Variational principles for involutive systems of vector fields

Abstract

In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar way by means of an higher order variational principle, and how this extends to involutive systems of vector fields.

31 pages. To appear in International Journal of Geometric Methods in Modern Physics (IJGMMP)

References in corpus (4)

• Exterior Differential Systems and Euler-Lagrange Partial Differential Equations
• Hyperhamiltonian dynamics
• A variational principle for volume-preserving dynamics
• Maximal degree variational principles