Broken ray transform for twisted geodesics on surfaces with a reflecting obstacle

TL;DR

This paper proves a uniqueness result for the broken ray transform on surfaces with reflecting obstacles, extending previous work to include twisted geodesic flows influenced by external forces.

Contribution

It generalizes the broken geodesic ray transform results to twisted geodesics, magnetic flows, and thermostats on surfaces with obstacles under nonpositive curvature.

Findings

Uniqueness of the broken ray transform for twisted geodesics

Extension to magnetic flows and thermostats

Applicable to surfaces with convex reflecting obstacles

Abstract

We prove a uniqueness result for the broken ray transform acting on the sums of functions and $1$-forms on surfaces in the presence of an external force and a reflecting obstacle. We assume that the considered twisted geodesic flows have nonpositive curvature. The broken rays are generated from the twisted geodesic flows by the law of reflection on the boundary of a suitably convex obstacle. Our work generalizes recent results for the broken geodesic ray transform on surfaces to more general families of curves including the magnetic flows and Gaussian thermostats.