  We study the geodesics of a five dimensional non-asymptotically flat
dilatonic 2-brane. Although the metric's warp function diverges logarithmically
in the far field region of the transverse space, the curvature does not. The
brane has two naked singularities, the usual central singularity and a circular
singularity at the radius where the warp function vanishes. This creates two
causally disconnected regions of the transverse space. Using the methods of
energy conservation and effective potentials we study the null and timelike
orbital and radial geodesics in both regions and show that they exhibit
opposing energy requirements.
