satisfies $X_t(\Lambda)=\Lambda$ for all $t\in{{\mathbb R}}$.

A *trapping region* $U$ for a flow $X_t$ is an open subset of the manifold $M$ which satisfies: $X_t(U)$ is contained in $U$ for all $t>0$; and there exists $T>0$ such that $\overline{X_t(U)} $ is contained in the interior of $U$ for all $t>T$. The maximal invariant set $\Lambda_X(U):= \cap_{t \geq 0} X_t(U)$ of $U$ is called an *attracting set*. An attracting set for $X$ which is transitive is called an *attractor* for $X$. A *repeller* for $X$ is an attractor for $-X$.

We say that a set $\Lambda$ is *Lyapunov stable* if for every neighborhood $U$ of $\Lambda$ there is another one $V \subset U$ such that every point $p \in V$ has its forward orbit contained in $U$.

A *singularity* for the vector field $X$ is a point $\sigma\in M$ such that $X(\sigma)=0$ or, equivalently, $X_t(\sigma)=\sigma$ for all $t \in {{\mathbb R}}$. The set formed by singularities is the *singular set of $X$* denoted ${\mathrm{Sing}}(X)$ and ${\operatorname{Per}}(X)$ is the set of periodic points of $X$. We say that a *singularity is hyperbolic* if the eigenvalues of the derivative $DX(\sigma)$ of the vector field at the singularity $\sigma$ have nonzero real part. The 