  For any $\theta, \omega > 1/2$ we prove that, if any $d$-pseudotrajectory of
length $\sim 1/d^{\omega}$ of a diffeomorphism $f\in C^2$ can be
$d^{\theta}$-shadowed by an exact trajectory, then $f$ is structurally stable.
Previously it was conjectured by Hammel-Grebogi-Yorke that for $\theta = \omega
= 1/2$ this property holds for a wide class of non-uniformly hyperbolic
diffeomorphisms. In the proof we introduce the notion of sublinear growth
property for inhomogenious linear equations and prove that it implies
exponential dichotomy.
