A short proof of ergodicity of Babillot-Ledrappier measures

Abstract

Let $M$ be a compact manifold, and let ${\phi _t}$ be a transitive homologically full Anosov flow on $M$. Let $\widetilde {M}$ be a $\mathbb {Z}^d$-cover for $M$, and let $\widetilde {\phi _t}$ be the lift of ${\phi _t}$ to $\widetilde {M}$. Babillot and Ledrappier exhibited a family of measures on $\widetilde {M}$, which are invariant and ergodic with respect to the strong stable foliation of $\widetilde {\phi _t}$. We provide a new short proof of ergodicity.