# Kupka-Smale theorem

Let $M$ be a compact smooth manifold^{}, and let ${\mathrm{Diff}}^{k}(M)$ denote the space of ${\mathcal{C}}^{k}$ diffeomorphisms from $M$ to itself. For every $k\in \mathbb{N}$, the set of Kupka-Smale diffeomorphisms is residual (http://planetmath.org/Residual) in the ${\mathcal{C}}^{k}$ Whitney topology of ${\mathrm{Diff}}^{k}(M)$.

Title | Kupka-Smale theorem |
---|---|

Canonical name | KupkaSmaleTheorem |

Date of creation | 2013-03-22 13:41:16 |

Last modified on | 2013-03-22 13:41:16 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 7 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 37C20 |

Related topic | KupkaSmale |