  Consider an analytical function $f:V\subset\mathbb R^2\rightarrow\mathbb R$
having $0$ as its regular value, a switching manifold $\Sigma=f^{-1}(0)$ and a
piecewise analytical vector field $X=(X^+,X^-)$, i.e. $X^\pm$ are analytical
vector fields defined on $\Sigma^\pm=\{p\in V: \pm f(p)>0\}$. We characterize
when the vector field $X$ has a monodromic singular point in $\Sigma$, called
$\Sigma$-monodromic singular point. Moreover, under certain conditions, we show
that a $\Sigma$-monodromic singular point of $X$ has a neighborhood free of
limit cycles.
