Please see: Maruskin, Jared M., Daniel J. Scheeres, and Anthony M. Bloch. "Dynamics of symplectic subvolumes." SIAM Journal on Applied Dynamical Systems 8.1 (2009): 180-201.
Scheeres, D. J., et al. "Fundamental limits on spacecraft orbit uncertainty and distribution propagation." The Journal of the Astronautical Sciences 54.3-4 (2006): 505-523.
These papers discuss some cases.