  We obtain numerical solutions for rotating topological solitons of the
nonlinear $\sigma$-model in three-dimensional Anti-de Sitter space. Two types
of solutions, $i)$ and $ii)$, are found. The $\sigma$-model fields are
everywhere well defined for both types of solutions, but they differ in their
space-time domains. Any time slice of the space-time for the type $i)$ solution
has a causal singularity, despite the fact that all scalars constructed the
curvature tensor are bounded functions. No evidence of a horizon is seen for
any of the solutions, and therefore the type $i)$ solutions have naked
singularities.
  On the other hand, the space-time domain, along with the fields, for the type
$ii)$ solutions are singularity free. Multiple families of solutions exhibiting
bifurcation phenomena are found for this case.
