# An Interval Eventually Bounding Trajectories of the Logistic Map

An Interval Eventually Bounding Trajectories of the Logistic Map

This Demonstration illustrates the iteration of the logistic map (x)=ax(1-x) for . All the points of the interval =(a/4,1) are mapped into =(0,a/4). Also, the interval =[(a/4),a/4] 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 .

h

a

2<a≤4

J

2

J

1

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4

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a

J

3

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4

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4