## Dynamics of closed singularities. (arXiv:1808.03219v1 [math.DG])

Parabolic geometric flows have the property of smoothing for short time
however, over long time, singularities are typically unavoidable, can be very
nasty and may be impossible to classify. The idea of this paper is that, by
bringing in the dynamical properties of the flow, we obtain also smoothing for
long time for generic initial conditions. When combined with our earlier paper
this allows us to show that, in an important special case, the singularities
are the simplest possible.
We take here the first steps towards understanding the dynamics of the flow.
The question of the dynamics of a singularity has two parts. One is: What are
the dynamics near a singularity? The second is: What is the long time behavior
of the flow of things close to the singularity. That is, if the flow leaves a
neighborhood of a singularity, is it possible for the flow to re-enter the same
neighborhood at a much later time? The first part is addressed in this paper,
while the second will be addressed elsewhe查看全文