Travelling Times in Scattering by Obstacles in Curved Space
Differential Geometry
2020-08-28 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2003.12261,
title = {Travelling Times in Scattering by Obstacles in Curved Space},
author = {Tal Gurfinkel and Lyle Noakes and Luchezar Stoyanov},
journal= {arXiv preprint arXiv:2003.12261},
year = {2020}
}