article published yes Péter Bálint author Jacopo De Simoi author Vadim Kaloshin author FE553552-CDE8-11E9-B324-C0EBE56974250000-0002-6051-2628 Martin Leguil author 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. Springer Nature2019 eng Mathematical PhysicsStatistical and Nonlinear Physics 0010-3616 1432-0916 1809.0894710.1007/s00220-019-03448-x 37431531-1575 yes Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications in Mathematical Physics. 374(3), 1531–1575. Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. <i>Communications in Mathematical Physics</i>. 2019;374(3):1531-1575. doi:<a href="https://doi.org/10.1007/s00220-019-03448-x">10.1007/s00220-019-03448-x</a> Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2019. <a href="https://doi.org/10.1007/s00220-019-03448-x">https://doi.org/10.1007/s00220-019-03448-x</a>. P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical Physics 374 (2019) 1531–1575. Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.” <i>Communications in Mathematical Physics</i>, vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:<a href="https://doi.org/10.1007/s00220-019-03448-x">10.1007/s00220-019-03448-x</a>. P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards,” <i>Communications in Mathematical Physics</i>, vol. 374, no. 3. Springer Nature, pp. 1531–1575, 2019. Bálint, P., De Simoi, J., Kaloshin, V., &#38; Leguil, M. (2019). Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s00220-019-03448-x">https://doi.org/10.1007/s00220-019-03448-x</a> 84152020-09-17T10:41:27Z2021-01-12T08:19:08Z