论文标题
通用凸体中的台球具有积极的拓扑熵
Billiards in generic convex bodies have positive topological entropy
论文作者
论文摘要
我们表明，存在一套$ C^2 $开放密集的凸面，并具有光滑的边界，其台球地图表现出非平凡的双曲线基本套件。结果，通用凸体中的台球具有正拓扑熵和周期轨道数量的指数增长。
We show that there exists a $C^2$ open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponential growth of the number of periodic orbits.
