Anosov flow

Summary

An Anosov flow is a flow on a compact manifold with a splitting of the tangent bundle into three parts. They are the flow direction, a uniformly contracted direction and a uniformly expanded direction. It is the continuous-time analogue of an Anosov diffeomorphism. The geodesic flow of a compact Riemannian manifold of negative sectional curvature is an Anosov flow, a fact proved by Anosov. Anosov flows are structurally stable up to orbit equivalence, and those of class $C^2$ that preserve a smooth volume are ergodic.