  We consider billiards obtained by removing three strictly convex obstacles
satisfying the non-eclipse condition on the plane. The restriction of the
dynamics to the set of non-escaping orbits is conjugated to a subshift on three
symbols that provides a natural labeling of all periodic orbits. We study the
following inverse problem: does the Marked Length Spectrum (i.e., the set of
lengths of periodic orbits together with their labeling), determine the
geometry of the billiard table? We show that from the Marked Length Spectrum it
is possible to recover the curvature at periodic points of period two, as well
as the Lyapunov exponent of each periodic orbit.
