论文标题
Minkowski倍曲面上的可集成台球：极端多项式和拓扑
Integrable Billiards on a Minkowski Hyperboloid: Extremal Polynomials and Topology
论文作者
论文摘要
我们考虑在Minkowski空间中的一张薄片上，紧凑型域中的台球系统。我们得出了此类台球的椭圆周期性条件。我们描述了这些台球系统的拓扑结构，该系统在Fomenko不变性方面。然后，我们就功能性PEL方程和相关的极端多项式提供了周期性条件。根据椭圆函数以及经典的Chebyshev和Zolotarev多项式计算了几个示例，作为一个或两个间隔的极端多项式。这些结果与Minkowski和Euclidean Planes中的台球病例形成鲜明对比。
We consider billiard systems within compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We derive conditions for elliptic periodicity for such billiards. We describe the topology of those billiard systems in terms of Fomenko invariants. We provide then periodicity conditions in terms of functional Pell equations and related extremal polynomials. Several examples are computed in terms of elliptic functions and classical Chebyshev and Zolotarev polynomials, as extremal polynomials over one or two intervals. These results are contrasted with the cases of billiards in the Minkowski and the Euclidean planes.
