Inverse Problems for Twisted Geodesic Flows

TL;DR

This paper surveys inverse problems associated with twisted geodesic flows on Riemannian manifolds, emphasizing generalized ray transforms, tensor tomography, and rigidity, to understand complex dynamical behaviors.

Contribution

It provides a comprehensive overview of inverse problems for twisted geodesic flows, highlighting recent advances and open questions in the field.

Findings

Overview of generalized ray transforms and their injectivity

Connections between tensor tomography and flow rigidity

Identification of key challenges in inverse problems for twisted flows

Abstract

The article surveys inverse problems related to the twisted geodesic flows on Riemannian manifolds with boundary, focusing on the generalized ray transforms, tensor tomography, and rigidity problems. The twisted geodesic flow generalizes the usual geodesic flow, allowing to model richer dynamics.