Universität Augsburg
Institut für Mathematik

Please ask Prof. Kai Cieliebak for­ login details.

A biliard model in a half plane, with the boundary line of the half plane as wall of reflection, defined via the planar Kepler problem, which can be viewed as a limiting case of a more complicated model proprosed by Boltzmann to illustrate his "ergodic hypothesis", is recently shown to be integrable by Gallavotti and Jauslin who explicitely constructed an independent integral additional to the energy. The bounded dynamics of the system has been shown by Felder to carry periodic and quasi-periodic dynamics. In this talk, I shall explain that the integral of Gallavotti-Jauslin is untimately related to the energy of an associated Kepler problem on the sphere. The approach is based on the projective dynamical properties of the Kepler problem. As an additional consequence, we define a class of integrable billiard systems on the sphere with the spherical Kepler problem and with a circle on the sphere as wall of reflection.