论文标题
球形楔形台球：从混乱到分形和塔尔伯特地毯
Spherical wedge billiard: from chaos to fractals and Talbot carpets
论文作者
论文摘要
我们介绍了球形楔形台球，这是一个动态系统，该系统由沿球形楔形的封闭的非欧几里得表面上的大地测量物移动。我们得出相应的庞加莱图的分析形式，并找到了非常复杂的动力学，从完全混乱到非常规定的分形特征。此外，我们表明，在更改台球参数后，庞加莱地图的固定点以复杂的方式合并，这起源于台球映射的球形畸变。当相位图与塔尔伯特地毯密切相关时，我们还详细分析了常规状态。
We introduce the spherical wedge billiard, a dynamical system consisting of a particle moving along a geodesic on a closed non-Euclidean surface of a spherical wedge. We derive the analytic form of the corresponding Poincaré map and find very complex dynamics, ranging from completely chaotic to very regular, exhibiting fractal features. Further, we show that upon changing the billiard parameter, the fixed points of the Poincaré map merge in complex ways, which has origin in the spherical aberration of the billiard mapping. We also analyze in detail the regular regime when phase space diagram is closely related to Talbot carpets.
