A 1-D Map often called ``the'' quadratic map is defined by

(1) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

The most general second-order 2-D Map with an elliptic fixed point at the origin has the form

(9) | |||

(10) |

The map must have a Determinant of 1 in order to be Area preserving, reducing the number of independent parameters from seven to three. The map can then be put in a standard form by scaling and rotating to obtain

(11) | |||

(12) |

The inverse map is

(13) | |||

(14) |

The Fixed Points are given by

(15) |

© 1996-9

1999-05-25