  The existence of critical points for the peculiar velocity field is a natural
feature of the correlated vector field. These points appear at the junctions of
velocity domains with different orientations of their averaged velocity
vectors. Since peculiar velocities are the important cause of the scatter in
the Hubble expansion rate, we propose that a more precise determination of the
Hubble constant can be made by restricting analysis to a subsample of
observational data containing only the zones around the critical points of the
peculiar velocity field, associated with voids and saddle points. On
large-scales the critical points, where the first derivative of the
gravitational potential vanishes, can easily be identified using the density
field and classified by the behavior of the Hessian of the gravitational
potential. We use high-resolution N-body simulations to show that these regions
are stable in time and hence are excellent tracers of the initial conditions.
Furthermore, we show that the variance of the Hubble flow can be substantially
minimized by restricting observations to the subsample of such regions of
vanishing velocity instead of aiming at increasing the statistics by averaging
indiscriminately using the full data sets, as is the common approach.
