An integrable deformation of an ellipse of small eccentricity is an ellipse

• 成果类型: Article
• 署名作者: Avila, Artur; De Simoi, Jacopo; Kaloshin, Vadim
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.184.2.5
• 发表日期: 2016
• 页码: 527-558
• 关键词: billiards; spectrum; shape; hear

摘要

The classical Birkhoff conjecture claims, that the boundary of strictly convox integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we show that a version of this conjecture is true for tables bounded by small perturbations of ellipses of small eccentricity.