  In earlier work, carrying out numerical simulations of the Ricci flow of
families of rotationally symmetric geometries on $S3$, we have found strong
support for the contention that (at least in the rotationally symmetric case)
the Ricci flow for a ``critical'' initial geometry - one which is at the
transition point between initial geometries (on $S^3$) whose volume-normalized
Ricci flows develop a singular neck pinch, and other initial geometries whose
volume normalized Ricci flows converge to a round sphere - evolves into a
``degenerate neck pinch.'' That is, we have seen in this earlier work that the
Ricci flows for the critical geometries become locally cylindrical in a
neighborhood of the initial pinching, and have the maximum amount of curvature
at one or both of the poles. Here, we explore the behavior of these flows at
the poles, and find strong support for the conjecture that the Bryant steady
solitons accurately model this polar flow.
