Hyperbolciity of convex billiards
under random perturbations
报告专家：张宏坤教授（美国麻省大学/大湾区大学）
报告时间：2024年11月22日（星期五）上午10：00-11：00
报告地点：国家天元数学西南中心516报告厅
报告摘要：We consider convex billiards bounded by a simple, smooth, closed curve.These convex billiards are proven to have KAM islands, if the boundary is smooth enough.Even for non-smooth convex billiards, the hyperbolicity is rare. Some exceptions are the Bunimovich stadium, and certain Lemon billiards. Moreover, hyperbolicity is rather difficult to prove,mainly because of the focusing effect of the wavefront upon hitting the convex boundary.
In this work, we consider certain random perturbations of convex billiards, following a recent work by Roberto Markarian and collaborators,We are able to prove that a large number of billiards are hyperbolic.We also identify some billiards that can not be hyperbolic under such perturbations.
专家简介：张宏坤教授是研究双曲动力学系统（包括混沌台球）统计特性的专家。现代动力系统的一个主要趋势是研究混沌动力系统产生的随机过程的随机性质，包括相关衰减率、中心极限理论和其他概率极限定理。张宏坤教授在这一领域做出了许多有意义的工作，在《 Comm. Math. Phys.》，《 Trans. Amer. Math. Soc.》等国际权威杂志上发表论文40余篇。张宏坤教授的研究领域也扩展到一般的随机过程和概率论，SDE和统计学在金融数学中应用等。近年来，张宏坤教授的研究兴趣集中在动力系统和机器学习的交叉领域，取得了大量有意义的研究成果。
