Let $M$ be a Riemannian manifold, $f\colon M\to M$ a diffeomorphism and $\Lambda\subset M$ a compact hyperbolic set for $f$. Then there is a neighborhood $U$ of $\Lambda$ such that for every $\delta>0$ there is an $\epsilon>0$ so that every $\epsilon$-orbit (http://planetmath.org/PseudoOrbit) in $U$ is $\delta$-shadowed by an orbit of $f$.
Moreover, there is $\delta_{0}>0$ such that, if $\delta<\delta_{0}$ and if the pseudo-orbit is bi-infinite, then the shadowing orbit is unique; and if $\Lambda$ has a local product structure then the shadowing orbit is in $\Lambda$.