  We develop the characterization of the dynamics at the noise-perturbed edge
of chaos in logistic maps in terms of the quantities normally used to describe
glassy properties in structural glass formers. Following the recognition [Phys.
Lett. \textbf{A 328}, 467 (2004)] that the dynamics at this critical attractor
exhibits analogies with that observed in thermal systems close to
vitrification, we determine the modifications that take place with decreasing
noise amplitude in ensemble and time averaged correlations and in diffusivity.
We corroborate explicitly the occurrence of two-step relaxation, aging with its
characteristic scaling property, and subdiffusion and arrest for this system.
We also discuss features that appear to be specific of the map.
