  We study the time evolution of the survival probability $P(t)$ in open
one-dimensional quasiperiodic tight-binding samples of size $L$, at critical
conditions. We show that it decays algebraically as $P(t)\sim t^{-\alpha}$ up
to times $t^*\sim L^{\gamma}$, where $\alpha = 1-D_0^E$, $\gamma=1/D_0^E$ and
$D_0^E$ is the fractal dimension of the spectrum of the closed system. We
verified these results for the Harper model at the metal-insulator transition
and for Fibonacci lattices. Our predictions should be observable in propagation
experiments with electrons or classical waves in quasiperiodic superlattices or
dielectric multilayers.
