  A fluid of N smooth, hard spheres is considered as a model for normal
(elastic collisions) and granular (inelastic collisions) fluids. The potential
energy is discontinuous for hard spheres so the pairwise forces are singular
and the usual forms of Newtonian and Hamiltonian mechanics do not apply.
Nevertheless, particle trajectories in the N particle phase space are well
defined and the generators for these trajectories can be identified. The first
part of this presentation is a review of the generators for the dynamics of
observables and probability densities. The new results presented in the second
part refer to applications of these generators to the Liouville dynamics for
granular fluids. A set of eigenvalues and eigenfunctions of the generator for
this Liouville dynamics is identified in a special "stationary representation".
This provides a class of exact solutions to the Liouville equation that are
closely related to hydrodynamics for granular fluids.
