accumulation point

LEMMA 5.2 Let X be a Hausdorff space and A a subset of X. A point a∈X is an accumulation point of A if and only if a is a limit point of A.

The chaotic set (not necessarily attracting) is formed after the first accumulation point (a_∞≈3.570 for the logistic mapping) is reached. In the chaotic region of the logistic map the periodicity re-emerges in periodic windows which are bounded by the accumulation point from the right and by the saddle-node bifurcation from the left. A reverse bifurcation sequence occurs above the accumulation point.