Universality of the window structure and the density of aperiodic solutions in dissipative dynamical systems

The structure of periodic windows in one-dimensional maps is shown to become quantitatively universal approaching a period-doubling accumulation point from the opposite side. This implies, among other things, that the relative density of aperiodic solutions tends to a universal number =0.892.... This universality of the window structure applies to the same class of maps as the period-doubling universality, and we have strong numerical evidence for it to apply to any dissipative multidimensional dynamics which goes through a complete period-doubling sequence.