Deterministic Chaos

6.D.5. Return Map

Recall in our presentation of graphical iteration, the pair of thick green lines connects (xn, xn) to (xn+1, xn+1).
To generate the return map, we want to plot a point with y-coordinate xn+1 and x-coordinate xn.
The horizontal line from (xn+1, xn+1) (the end of the horizontal green graphical iteration line) consists of points all with y-coordinate xn+1.
The horizontal line from (xn, xn) (the beginning of the vertical green graphical iteration line) consists of points all with y-coordinate xn.
This orange line intersects the diagonal in the return map square at the point (xn, xn).
The vertical line from this point consists of points with x-coordinate xn.
Consequently, the vertical orange line and horizontal light blue line intersect at the point (xn, xn+1), a point of the return map.

Return to the Return Map.