# Hartman-Grobman theorem

Let $U$ and $V$ be open subsets of a Banach space $E$ such that $0\in U\cap V$.
If a diffeomorphism^{} $f:U\to V$ has $0$ as a hyperbolic fixed
point^{}, then $f$ and $Df(0)$ are locally topologically conjugate^{} at $0$,
i.e. there are neighborhoods^{} $\stackrel{~}{U}$ and $\stackrel{~}{V}$ of $0$ and a homeomorphism^{} $h:\stackrel{~}{U}\to \stackrel{~}{V}$ such that
$Df(0)h=hf$.

Title | Hartman-Grobman theorem |
---|---|

Canonical name | HartmanGrobmanTheorem |

Date of creation | 2013-03-22 14:25:15 |

Last modified on | 2013-03-22 14:25:15 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 6 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 37C25 |

Synonym | Grobman-Hartman theorem |

Synonym | Hartman’s theorem |