Koopman-von Neumann formalism meets contact Hamiltonian systems

The present work develops a Koopman--von Neumann (KvN) formulation of contact Hamiltonian dynamics on the Hilbert space defined by the contact volume. The resulting generator includes the divergence correction required for unitary evolution. We establish symmetry and, for complete contact Hamiltonian vector fields, essential self-adjointness and a strongly continuous unitary evolution; we also describe covariance under contactomorphisms. For completely integrable contact systems with complete flows, it is possible to recover an invariant direct-integral decomposition and strongly commuting KvN generators. We further relate contact KvN dynamics to the KvN formulation of its symplectization.