  We present an analytical description of the motion in the singular
logarithmic potential. This potential plays an important role in the modeling
of triaxial systems (like elliptical galaxies) or bars in the centers of galaxy
disks. In order to obtain information about the motion near the singularity, we
resort to McGehee -type transformations and regularize the vector field. In the
axis-symmetric case (b=1), we offer a complete description of the global
dynamics. In the non axis-symmetric case (b<1), we prove that all orbits, with
the exception of a negligible set, are centrophobic and retrieve numerically
partial aspects of the orbital structure.
