  We have studied numerically the Hamiltonian dynamics of two same-sign point
vortices in an effectively two-dimensional, harmonically trapped Bose-Einstein
condensate. We have found in the phase space of the system an impenetrable wall
that divides the dynamics into two distinct and exhaustive types. In the
two-dimensional position-coordinate space, the first type corresponds to
intersecting single-vortex orbits and the second type to orbits that have no
points in common. The two types are also easily distinguished in the
two-dimensional space spanned by the radial and angular velocities of the
vortices: in the first type, both single-vortex orbits are the same simple loop
in this two-dimensional space, whereas in the second type the two orbits
constitute two nonintersecting loops. The phase-space-dividing wall is distinct
from the bifurcation curve of rigidly rotating states found by Navarro et al.
[Phys. Rev. Lett. 110, 225301 (2013)].
