Circle Packing and Hamiltonian Mappings
An area-preserving map is derived from a kicked Hamiltonian. The map shows circular orbits in phase space similar to circle packings.
The Hamiltonian with parameter and kicks represented by a sequence of Dirac delta functions is
where , , and are the position, momentum, and time. The map then takes the form
 A. J. Scott, C. A. Holmes, and G. J. Milburn, "Hamiltonian Mappings and Circle Packing Phase Spaces," Physica D, 155(1–2), 2001 pp. 34–50. doi:10.1016/S0167-2789(01)00263-9.
 G. Hughes, "Outer Billiards, Digital Filters and Kicked Hamiltonians," 2012. arxiv.org/abs/1206.5223.
 "Dynamics of Polygons." (Feb 26, 2013) dynamicsofpolygons.org.