论文标题
介绍次曼尼亚和子罚款台球
Introducing sub-Riemannian and sub-Finsler Billiards
论文作者
论文摘要
我们在子鳍几何形状的背景下定义台球。我们提供了对问题的符合性和变分（或者控制理论）描述，并表明它们是重合的。然后，我们在这种情况下讨论了几种现象，包括在边界分布的单数点，滑行和爬行轨道的出现以及在波前的反射行为，在边界分布的奇异点上未能明确定义。然后，我们研究了具有标准接触结构的三维欧几里得空间中的一些混凝土表。这些可以解释为具有不同磁强度的平面磁性台球，在反射下可能会改变磁强度。对于每个表，我们提供有关周期轨迹，滑行轨道和蠕变轨道的各种结果。
We define billiards in the context of sub-Finsler Geometry. We provide symplectic and variational (or rather, control theoretical) descriptions of the problem and show that they coincide. We then discuss several phenomena in this setting, including the failure of the reflection law to be well-defined at singular points of the boundary distribution, the appearance of gliding and creeping orbits, and the behavior of reflections at wavefronts. We then study some concrete tables in 3-dimensional euclidean space endowed with the standard contact structure. These can be interpreted as planar magnetic billiards, of varying magnetic strength, for which the magnetic strength may change under reflection. For each table we provide various results regarding periodic trajectories, gliding orbits, and creeping orbits.
