Lemma 7.2.7 from "Introduction to the Modern Theory of Dynamical Systems" - Katok & Hasselblatt:
Let $0 < r \leq k \leq \infty$ and $M$ a compact $C^k$ manifold. If $f : M \to M$ is a $C^k$ diffeomorphism that has only transverse periodic points of period $n$ and $\epsilon > 0$, then there exists $g : M \to M$ a $C^k$ diffeomorphism having only hyperbolic periodic points of period $n$ and $\epsilon$-close to $f$ in the $C^r$ topology.
Can someone tell me where can I find the proof of this Lemma and the proof of Kupka - Smale Theorem? I want a source different of Katok & Hasselblatt, with more details.