Detection of all low-period windows for the logistic map

A systematic method to find all low-period windows for the logistic map f_a(x) = ax(1 - x) is proposed. The method is used to obtain very good approximations of positions of periodic windows with periods p ≤ 20. For each window using the forward shooting based interval Newton operator we confirm its existence by proving the existence of a sink for several parameter values inside the window and compute a very accurate rigorous lower bound of the window width.