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

Marked Length Spectrum, homoclinic orbits and the geometry of open dispersing billiards