On a smooth manifold of dimension n,the application value of the canonical 1-form,the Liouville form
on T*(X) to the Hamiltonian mechanics is well known;T*(X) is a degree 1-Jet bundle.My question is
Do canonical forms similar to the Liouville form exist on higher degree Jet bundles?
I ask this because,beyond the invariant sub-principal symbol of a Pseudodifferential Operator,
nothing much seems to be known to handle multiple characteristic problems specially of the non-involutive
type.Iam aware of Ivrii-type Fuchsian operators,already posing great difficulties.
Should be grateful for inputs-Nagaraj Iyengar,community wiki