On the Integrability of Strictly Convex Billiard Tables with Boundaries Close to Ellipses with Small Eccentricities

• 作者: Guan HUANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 55-67
• 页数: 13页
• 语种: 英文

摘要

In this paper,we introduce a new notion of integrability for billiard tables,namely,inte-grability away from the boundary.One key feature of our notion is that the integrable region could be disjoint from the boundary with a positive distance.We prove that if a strictly convex billiard table,whose boundary is a small perturbation of an ellipse with small eccentricity,is integrable in this sense,then its boundary must be itself an ellipse.