An upper bound for the mean Lorentz force of magnetic flows without conjugate points in terms of the geodesic curvature of horocycles

We study magnetic flows on closed Riemannian surfaces of genus at least two. Let $(M,g)$ be a surface without focal points and let $Ω$ be a magnetic field. We prove that, above the Mañé critical value, the absence of conjugate points imposes geometric restrictions on the magnetic flow. First, we obt