Dynamical spectral rigidity among Z2 -symmetric strictly convex domains close to a circle

• 成果类型: Article
• 署名作者: De Simoi, Jacopo; Kaloshin, Vadim; Wei, Qiaoling
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.186.1.7
• 发表日期: 2017
• 页码: 277-314
• 关键词: isospectral sets; SURFACES; shape; hear

摘要

We show that any sufficiently (finitely) smooth Z(2) -symmetric strictly convex domain sufficiently close to a circle is dynamically spectrally rigid; i.e., all deformations among domains in the same class that preserve the length of all periodic orbits of the associated billiard flow must necessarily be isometric deformations. This gives a partial answer to a question of P. Sarnak.