The Magnetic Ray Transform on Anosov Surfaces

TL;DR

This paper investigates the magnetic ray transform on Anosov surfaces, proving its injectivity for low-degree tensors and exploring implications for magnetic flow entropy under perturbations.

Contribution

It establishes surjectivity of the adjoint magnetic ray transform and proves injectivity for tensors up to degree two on Anosov surfaces.

Findings

Injectivity of the magnetic ray transform for tensors of degree at most two.

Surjectivity results for the adjoint magnetic ray transform.

Application to entropy production in perturbed magnetic flows.

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.