  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.
