Marked Length Spectral determination of analytic chaotic billiards with axial symmetries

We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift, which provides a natural labeling of periodic orbits. We show that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.

Automated summary

This passage discusses billiards obtained by removing finitely many strictly convex analytic obstacles from the plane, satisfying the non-eclipse condition. The dynamics restricted to the set of non-escaping orbits is conjugated to a subshift, which naturally labels periodic orbits. We demonstrate that under suitable symmetry and genericity assumptions, the Marked Length Spectrum determines the geometry of the billiard table.