The Magnetic Ray Transform on Anosov Surfaces

Abstract

Assume (M,g,Ω) is a closed, oriented Riemannian surface equipped with an Anosov magnetic flow. We establish certain results on the surjectivity of the adjoint of the magnetic ray transform, and use these to prove the injectivity of the magnetic ray transform on sums of tensors of degree at most two. In the final section of the paper we give an application to the entropy production of magnetic flows perturbed by symmetric 2-tensors.

arXiv comment15 pages; the previous version of this article contained an error in Proposition 2.2. The article has since been revised. All of the main ideas are retained and the main result on the injectivity of I_{2} on Anosov surfaces still holds. The injectivity of the ray transform on surfaces of negative magnetic curvature has been weakened from k-tensors to 2-tensors