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.

Posted on Aug 7, 2025 in Dynamical Systems, Seminars