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An Anosov flow is a nonsingular smooth flow on a compact smooth manifold with a continuous derivative-invariant splittingHere $F$ is the generating vector field, the flow direction is one-dimensional, and in the usual nontrivial convention both $E^s$ and $E^u$ have positive dimension. Constants $C,\lambda >0$ must work uniformly over all points, all $t\ge 0$ and the corresponding tangent vectors:The stable bundle of an Anosov flow contracts forward; the unstable bundle of an Anosov flow contracts backward. The neutral direction along $F$ is essential: changing the starting point slightly along an orbit mainly shifts its clock, so that direction cannot be included in either uniform contraction estimate.

A suspension flow of the cat map gives a three-dimensional example. A positive time change of a smooth flow preserves the Anosov property on a compact manifold, although its stable and unstable bundles can tilt along the flow direction. These are uniform structural conditions, stronger than a sign observed in one finite-time Lyapunov exponent calculation.