Parameters for two-parabolic Schottky Groups

Our main result is a description of the boundary of the parameter space of classical Schottky groups affording two parabolic generators within the larger parameter space of all Schottky groups with two parabolic generators. This boundary is surprisingly different from that of the larger space. It is analytic while the boundary of the larger space is fractal. Approaching the boundary of the smaller space does not correspond to pinching, circles become tangent but parabolics to not develop. As an application we construct an explicit one parameter family of non-classical Schottky groups. The existence of non-classical Schottky groups was proved by Marden [18], but until now only one example of such a group was known [29]. Other published constructions have turned out to be wrong.