Rigorous numerical study of the density of periodic windows for the logistic map.

Abstract

Numerical study of periodic windows for the logistic map is carried out. Accurate rigorous bounds for periodic windows' end points are computed using interval arithmetic based tools. An efficient method to find the periodic window with the smallest period lying between two other periodic windows is proposed. The method is used to find periodic windows extremely close to selected points in the parameter space and to find a set of periodic windows to minimize the maximum gap between them. The maximum gap reached is 4×10-9. The phenomenon of the existence of regions free from low-period windows is explained.