  The planar $N$-centre problem describes the motion of a particle moving in
the plane under the action of the force fields of $N$ fixed attractive centres:
\[
  \ddot{x}(t)=\sum_{j=1}^N\nabla V_j(x-c_j). \]
  In this paper we prove symbolic dynamics at slightly negative energy for an
$N$-centre problem where the potentials $V_j$ are positive, anisotropic and
homogeneous of degree $-\alpha_j$: \[
V_j(x)=|x|^{-\alpha_j}V_j\left(\frac{x}{|x|}\right). \] The proof is based on a
broken geodesics argument and trajectories are extremals of the Maupertuis'
functional.
  Compared with the classical $N$-centre problem with Kepler potentials, a
major difficulty arises from the lack of a regularization of the singularities.
We will consider both the collisional dynamics and the non collision one.
Symbols describe geometric and topological features of the associated
trajectory.
