标题： 台球与霍弗几何 显示英文标题

标题： Billiards and Hofer's Geometry

摘要： 我们提出了一种凸平面区域中的台球与Hofer几何之间的联系，这是辛拓扑的一个领域。 对于光滑严格凸的台球桌，我们证明了相应的台球球映射之间的Hofer距离在表之间的简单几何距离方面有一个上界。 我们利用这个结果来表明，凸多边形的台球球映射位于环面的光滑保面积映射群关于Hofer度量的完成中。 最后，我们讨论了与动力学相关的联系并提出了几个开放问题。 显示英文摘要

摘要： We present a link between billiards in convex plane domains and Hofer's geometry, an area of symplectic topology. For smooth strictly convex billiard tables, we prove that the Hofer distance between the corresponding billiard ball maps admits an upper bound in terms of a simple geometric distance between the tables. We use this result to show that the billiard ball map of a convex polygon lies in the completion, with respect to Hofer's metric, of the group of smooth area-preserving maps of the annulus. Finally, we discuss related connections to dynamics and pose several open problems.