Quasi-Fuchsian flows and the coupled vortex equations

We provide an alternative construction of the quasi-Fuchsian flows introduced by Ghys in \cite{Ghys-92}. Our approach is based on the coupled vortex equations that allows to see these flows as thermostats on the unit tangent bundle of the Blaschke metric uniquely determined by a conformal class and a holomorphic quadratic differential. We also give formulas for the marked length spectrum of a quasi-Fuchsian flow in the thermostat parametrization.