Marked Length Spectral determination of analytic chaotic billiards with axial symmetries

• 成果类型: Article
• 署名作者: De Simoi, Jacopo; Kaloshin, Vadim; Leguil, Martin
• 署名单位: University of Toronto; Institute of Science & Technology - Austria; Universite de Picardie Jules Verne (UPJV); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01191-8
• 发表日期: 2023
• 页码: 829-901
• 关键词: invariants; RIGIDITY; SCATTERING; domains; SINGULARITIES; SURFACES; shape; hear

摘要

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.