Travelling times in scattering by obstacles

The paper deals with some problems related to recovering information about an obstacle in a Euclidean space from certain measurements of lengths of generalised geodesics in the exterior of the obstacle. The main result is that if two obstacles satisfy some generic regularity conditions and have (almost) the same travelling times, then the generalised geodesic flows in their exteriors are conjugate on the non-trapping part of their phase spaces with a time preserving conjugacy. Apart from that a constructive procedure is described that shows how to recover an obstacle consisting of two convex domains in the plane from travelling times.