Twisted Ruelle zeta function at zero

I will talk about work in progress with Gabriel Paternain. The talk will discuss the order at zero of the Ruelle zeta function for Anosov flows on three manifolds, twisted with a unitary connection. I will recall the microlocal approach to hyperbolic dynamics and discuss how to compute the dimensions of resonant states for differential forms. The final result depends on topological and dynamical data.