论文标题
一张纸的倍数曲线中的伪 - 欧几里得台球
Pseudo-Euclidean Billiards within Confocal Curves on the Hyperboloid of One Sheet
论文作者
论文摘要
我们考虑了一个紧凑型域的台球问题，该域被共聚焦锥体界定在Minkowski空间中的一张薄片上。我们表明，在这种情况下，共聚焦家庭有两种类型。使用代数几何集成技术，我们证明每种类型的广义椭圆中的台球在liouville的意义上都是可以集成的。此外，我们证明了poncleet定理的概括，并为周期性轨迹得出了Cayley型条件并探索几何后果。
We consider a billiard problem for compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We show that there are two types of confocal families in such setting. Using an algebro-geometric integration technique, we prove that the billiard within generalized ellipses of each type is integrable in the sense of Liouville. Further, we prove a generalization of the Poncelet theorem and derive Cayley-type conditions for periodic trajectories and explore geometric consequences.
