Caustics for inner and outer billiards

With a plane closed convex curve, T, we associate two area preserving twist maps: the (classical) inner billiard in T and the outer billiard in the exterior of T. The invariant circles of these twist maps correspond to certain plane curves: the inner and the outer caustics of T. We investigate how the shape of T determines the possible location of caustics, establish the existence of open regions which are free of caustics, and estimate fro below the size of these regions in terms of the geometry of T.