Deterministic Chaos

6.D.5. Return Map

A return map plot of a sequence x0, x1, x2, x3, ... is a plot of the points
(x0, x1), (x1, x2), (x2, x3), (x3, x4), ...
Here is an illustration of the return using graphical iteration, and an explanation of the parts of this diagram.
Click the picture for an animation.

To illustrate the sorts of things we can learn from a return map, here are some time series (left) and return maps (right).

uniform random chaotic tent map average of chaotic tent maps

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