Consider a 1-D Hamiltonian Map of the form

(1) |

(2) | |||

(3) |

Now, write

(4) |

(5) | |||

(6) |

Then the equations of motion become

(7) | |||

(8) |

Note that equations (7) and (8) are not Area-Preserving, since

(9) |

(10) | |||

(11) |

(12) |

which is Area-Preserving.

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1999-05-25