[*central charge of the theory*]{} [@Ceresole:1995jg]. Observe that the presence of the factor $X$ in the r.h.s. is crucial for it to have zero global Kähler weight, just as the l.h.s. Further observe that the $r$-dependence is only through the scalars $Z^{i}(r)$!

The r.h.s. of this system of differential equations depends only on the scalar fields $Z^{i}$, and, thus, it is an autonomous system of ordinary differential equations[^9] that has fixed points $Z^{i}_{\rm
  fix}$ at the values at which the r.h.s. vanishes

$$\label{eq:attractorequations}
\left. \mathfrak{D}_{i}\mathcal{Z}\right|_{Z^{i}=Z^{i}_{\rm fix}}=0\, .$$

If the solution of this system of equations exists, it gives the fixed values of the scalars $Z^{i}_{\rm fix}$ as functions of the electric and magnetic charges only

$$Z^{i}_{\rm fix}= Z^{i}_{\rm fix}(q)\, ,$$

since the asymptotic values (moduli) $Z^{i}_{\infty}$ do not occur in the above differential equation. The fixed values are reached by the scalars at the value $\rho=\infty$, i.e. $r=0$, which is where the event horizon would be, as discussed at the beginning of this section and in what follows.

The fixed values may or may not be admissible, i.e. they may or may not belong to the definition domain of the complex coordinates $Z^{i}$. If the asymptotic values $Z^{i}_{\infty}$ are admissible 