# locally maximal

Let $f:M\to M$ be a diffeomorphism^{} of a smooth manifold $M$, and let $\mathrm{\Lambda}$ be a hyperbolic set for $f$. We say that $\mathrm{\Lambda}$ is *locally maximal* or *basic* if there exists a neighborhood^{} $U$ of $\mathrm{\Lambda}$ such that

$$\mathrm{\Lambda}=\bigcap _{n=-\mathrm{\infty}}^{\mathrm{\infty}}{f}^{n}(\overline{U}).$$ |

Title | locally maximal |
---|---|

Canonical name | LocallyMaximal |

Date of creation | 2013-03-22 14:07:24 |

Last modified on | 2013-03-22 14:07:24 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 5 |

Author | Koro (127) |

Entry type | Definition |

Classification | msc 37B35 |

Classification | msc 37D05 |

Synonym | basic set |