Realization of Local Contactomorphisms

Determine whether every local contactomorphism of a projective contact manifold can be realized as an outer contact billiard map over a suitable table.

Background

The paper proves that an outer contact billiard correspondence is a contactomorphism whenever it is a local diffeomorphism. The converse realization problem asks whether arbitrary local contact dynamics can arise from the characteristic-line and harmonic-conjugation construction associated with some table.