The magnetic ray transform on Anosov surfaces

Gareth Ainsworth

doi:10.3934/dcds.2015.35.1801

Article Contents

2015, Volume 35, Issue 5: 1801-1816. Doi: 10.3934/dcds.2015.35.1801

This issue Previous Article On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory Next Article Actions of solvable Baumslag-Solitar groups on surfaces with (pseudo)-Anosov elements

The magnetic ray transform on Anosov surfaces

Gareth Ainsworth^1,

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

Received: April 30, 2013

Revised: September 30, 2013

Published: May 2017

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Abstract

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.

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Mathematics Subject Classification: 53C25, 53C21, 53C22.

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