In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry–Mather periodic orbits of the induced billiard map from the (maximal) marked length spectrum of the domain.
"On the marked length spectrum of generic strictly convex billiard tables." Duke Math. J. 167 (1) 175 - 209, 15 January 2018. https://doi.org/10.1215/00127094-2017-0038