  We consider the class of dispersing billiard systems in the plane formed by
removing three convex analytic scatterers satisfying the non-eclipse condition.
The collision map in this system is conjugated to a subshift, providing a
natural labeling of periodic points. We study the problem of marked length
spectrum rigidity for this class of systems. We show that two such systems have
the same marked length spectrum if and only if their collision maps are
analytically conjugate to each other near a homoclinic orbit and that two
scatterers and the marked length spectrum together uniquely determine the third
scatterer.
