= Anosov diffeomorphism
{c}
{title2=$TM=E^s\oplus E^u,\quad \|Df^n|_{E^s}\|,\|Df^{-n}|_{E^u}\|\le Ce^{-\lambda n}$}
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An Anosov diffeomorphism is a continuously differentiable <diffeomorphism> of a compact <smooth manifold> with an invariant splitting of its <tangent bundle> into stable and unstable <vector subbundles> satisfying the displayed uniform exponential estimates for $n\ge0$, with $C,\lambda>0$. <Hyperbolic toral automorphisms> give examples. An <Anosov flow> has a further one-dimensional invariant bundle along the flow direction; its definition is a distinct continuous-time version of uniform hyperbolicity.
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