Linearized marked length spectrum rigidity for general Anosov flows.

RESUMEN: In this talk I will present some work in progress in a linearized version of the marked length spectrum rigidity for general Anosov flows (also known as Burns-Katok conjecture). I will begin with an introduction to the microlocal techniques used by Guillarmou and Lefeuvre to solve the problem in the case where metrics of negative curvature are close enough. Then, I will show how to generalize some aspects from the geodesic flow to more general ones, as the magnetic or thermostat flows, under some reasonable dynamical assumptions.