# An Interval Eventually Bounding Trajectories of the Logistic Map

Initializing live version

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration illustrates the iteration of the logistic map for . All the points of the interval are mapped into . Also, the interval is mapped into itself. If an iteration belongs to it can be proved that after a finite number of steps the trajectory is contained in . Therefore every trajectory whose starting point belongs to (0, 1) is eventually contained in

Contributed by: Lesinigo Matteo (March 2011)

Open content licensed under CC BY-NC-SA