I have already finished understanding the Poincaré-Bendixson theorem as a consequence of Schwartz's theorem, but I also want to analyze the example that Denjoy gave in $C^1$ that is not within the case taken in Schwartz's theorem. Does anyone know where I can find that detailed example? or maybe some generalization of this example? I would like to review it in detail to finish closing the idea of why Schwartz's theorem cannot be valid for flows of class $C^1$.

**Schwartz Theorem.-** Let $M$ be a compact, connected, two-dimensional manifold of class $C^2$. Let $\alpha: \mathbb R \times M \to M$ be a $C^2$ flow on $M$. Let $\Omega \subset M$ be an $\alpha$-minimal set. Then $\Omega$ must be one of the following:

$a)$ a singleton consisting of a fixed point

$b)$ a single, closed orbit homeomorphic to $S^1$

$c)$ all of $M$ which is homeomorphic to a torus $T^2$