# American Institute of Mathematical Sciences

May  2015, 35(5): 1801-1816. doi: 10.3934/dcds.2015.35.1801

## The magnetic ray transform on Anosov surfaces

 1 Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, CB3 0WB, United Kingdom

Received  May 2013 Revised  October 2013 Published  December 2014

Assume (M,g,$\Omega$) 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.
Citation: Gareth Ainsworth. The magnetic ray transform on Anosov surfaces. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 1801-1816. doi: 10.3934/dcds.2015.35.1801
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