Scattering rigidity for analytic Riemannian manifolds with a possible magnetic field

Abstract

Consider a compact Riemannian manifold with boundary endowed with a magnetic field. A path taken by a particle of unit charge, mass, and energy is called a magnetic geodesic. It is shown that if everything is real-analytic, the topology, metric, and magnetic field are uniquely determined by the scattering relation of the magnetic geodesic flow, measured at the boundary. Conjugate points are allowed with minor restrictions. In exchange for the real-analytic assumption, prior results in boundary rigidity are greatly generalized.