论文标题
弯曲空间中障碍物散射的旅行时间
Travelling Times in Scattering by Obstacles in Curved Space
论文作者
论文摘要
我们考虑在二维Riemannian歧管M上在障碍物K外部的台球轨迹的旅行时间M。我们证明，在其各自相位空间的非捕获部分上的两个障碍物几乎具有相同的行进时间，将具有时间预留的异议。此外，如果M具有非阳性截面曲率，我们会证明，如果K和L是两个严格凸边界的障碍，并且几乎相同的行进时间相同，则K和L是相同的。
We consider travelling times of billiard trajectories in the exterior of an obstacle K on a two-dimensional Riemannian manifold M. We prove that given two obstacles with almost the same travelling times, the generalised geodesic flows on the non-trapping parts of their respective phase-spaces will have a time-preserving conjugacy. Moreover, if M has non-positive sectional curvature we prove that if K and L are two obstacles with strictly convex boundaries and almost the same travelling times then K and L are identical.
