Marked Length Spectral determination of analytic chaotic billiards with axial symmetries

Abstract

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.

arXiv comment65 pages, 8 figures

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Cited by in corpus (2)

• Smooth conjugacy classes of 3D Axiom A flows
• Length Spectrum Rigidity for piecewise analytic Bunimovich Billiards