A geometrical version of the higher order Hamilton formalism in fibred manifolds (Q1077771)

The author makes more transparent the fact that an rth order Lagrangian on a fibered manifold \(Y\to X\) does not determine a unique Poincaré- Cartan form provided dim X\(>1\) and \(r>2\) by introducing a new operation generalizing the formal exterior differentiation. He deduces that a unique Poincaré-Cartan form can be determined by means of a simple additional structure - a linear symmetric connection \(\Gamma\) on the base manifold X. Further, by using a suitable geometric definition of a regular \(\gamma\) th order Lagrangian on Y he proves that any Poincaré- Cartan form can be used in the geometrical version of the higher order Hamilton formalism.