Abstract 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.

中文翻译：

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弯曲空间中障碍物散射的旅行时间

摘要 我们考虑了二维黎曼流形 M 上障碍物 K 外部的台球轨迹的行进时间。我们证明了给定两个行进时间几乎相同的障碍物，广义测地线在它们各自的非俘获部分上流动。相空间将具有时间保持共轭。此外，如果 M 具有非正截面曲率，我们证明如果 K 和 L 是两个具有严格凸边界且行进时间几乎相同的障碍物，则 K 和 L 是相同的。