Variational principles for involutive systems of vector fields

TL;DR

This paper explores how involutive systems of vector fields can be characterized using higher-order variational principles, extending the classical approach based on one-forms, with implications for areas like Hamiltonian dynamics.

Contribution

It introduces a novel higher-order variational framework for involutive systems of vector fields, generalizing the classical variational principles used in Hamiltonian dynamics.

Findings

Higher-order variational principles can characterize involutive systems.

Extension of classical variational methods to more complex vector field systems.

Potential applications in advanced dynamical systems analysis.

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.