Global Dynamics in the Singular Logarithmic Potential

We present an analytical description of the motion in the singular logarithmic potential of the form Φ = ln √ x1/b 2 + x2, a potential which 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 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.