Anosov flow
= Anosov flow
{c}
A nonsingular <smooth flow> on a compact <smooth manifold> is Anosov if there is a continuous invariant splitting $TN=E^s\oplus\mathbb RF\oplus E^u$ and constants $C,\lambda>0$ with $\|D\phi_t v_s\|\le Ce^{-\lambda t}\|v_s\|$ and $\|D\phi_{-t}v_u\|\le Ce^{-\lambda t}\|v_u\|$ for $t\ge0$. Uniform contraction and expansion are transverse to the neutral flow direction, which distinguishes the splitting from that of an <Anosov diffeomorphism>.