Lie-Poisson description of Hamiltonian ray optics (Q1181167)

For an axi-symmetric medium, the standard classical picture in the geometrical optics approximation as a Hamiltonian system is recast in the form of a Lie-Poisson dynamical system. This allows a geometric interpretation of essentially all relevant concepts in the Hamiltonian picture. This slightly ``dual'' framework renders the description of phenomena, a greater clarity in many cases, and a great number of the analogous geometrical concepts are carefully worked out by the authors.