A return map plot of a sequence
x_{0}, x_{1}, x_{2}, x_{3}, ... is a plot of the points |

_{0}, x_{1})_{1}, x_{2})_{2}, x_{3})_{3}, x_{4}) |

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 |

Return to Deterministic Chaos.