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arXiv · 2003.12261

Travelling Times in Scattering by Obstacles in Curved Space

Tal Gurfinkel·Lyle Noakes·Luchezar Stoyanov
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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.

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Tal Gurfinkel, Lyle Noakes, Luchezar Stoyanov. 2020-03-27. Travelling Times in Scattering by Obstacles in Curved Space. https://doi.org/10.1016/j.jde.2020.05.049

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