Universal features of tangent bifurcation

We exhibit certain universal characteristics of limit cycles pertaining to one-dimensional maps in the 'chaotic' region beyond the point of accumulation connected with period doubling. Universal, Feigenbaum-type numbers emerge for different sequences, such as triplication. More significantly, we have established the existence of different classes of universal functions which satisfy the same renormalization group equations, with the same parameters, as the appropriate accumulation point is reached.