# Kupka-Smale theorem

Let $M$ be a compact smooth manifold, and let $\operatorname{Diff}^{k}(M)$ 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 $\operatorname{Diff}^{k}(M)$.

Title Kupka-Smale theorem KupkaSmaleTheorem 2013-03-22 13:41:16 2013-03-22 13:41:16 Koro (127) Koro (127) 7 Koro (127) Theorem msc 37C20 KupkaSmale