# attracting fixed point

Let $X$ be a vector field on a manifold $M$ and let ${F}_{t}$ be the flow of $X$. A fixed point^{} ${x}^{*}$ of $X$ is called attracting if there exists a neighborhood^{} $U$ of ${x}^{*}$ such that for every $x\in U$, ${F}_{t}(x)\to {x}^{*}$ as $t\to \mathrm{\infty}$.

The stability of a fixed point can also be classified as stable, unstable, neutrally stable, and Liapunov stable.

Title | attracting fixed point |
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Canonical name | AttractingFixedPoint |

Date of creation | 2013-03-22 13:06:24 |

Last modified on | 2013-03-22 13:06:24 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 6 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 37C75 |

Related topic | GloballyAttractingFixedPoint |

Related topic | LiapunovStable |

Related topic | StableFixedPoint |

Related topic | NeutrallyStableFixedPoint |

Related topic | UnstableFixedPoint |