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 sho...

Full description

Saved in:
Bibliographic Details
Published in:Inventiones mathematicae 2023-08, Vol.233 (2), p.829-901
Main Authors: De Simoi, Jacopo, Kaloshin, Vadim, Leguil, Martin
Format: Article
Language:English
Subjects:
Billiards
Geometry
Mathematics
Mathematics and Statistics
Orbits
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-023-01191-8