# homoclinic

If $X$ is a topological space^{} and $f$ is a flow on $X$ or an homeomorphism^{} mapping $X$ to itself, we say that $x\in X$ is an homoclinic point (or homoclinic intersection) if it belongs to both the stable and unstable sets of some fixed or periodic point $p$; i.e.

$$x\in {W}^{s}(f,p)\cap {W}^{u}(f,p).$$ |

The orbit of an homoclinic point is called an homoclinic orbit.

Title | homoclinic |
---|---|

Canonical name | Homoclinic |

Date of creation | 2013-03-22 13:48:35 |

Last modified on | 2013-03-22 13:48:35 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 5 |

Author | Koro (127) |

Entry type | Definition |

Classification | msc 37C29 |