  We describe precisely, under generic conditions, the contact of the
accessibility set at time $T$ with an abnormal direction, first for a
single-input affine control system with constraint on the control, and then as
an application for a sub-Riemannian system of rank 2. As a consequence we
obtain in sub-Riemannian geometry a new splitting-up of the sphere near an
abnormal minimizer $\gamma$ into two sectors, bordered by the first
Pontryagin's cone along $\gamma$, called the $\xLinfty$-sector and the
$\xLtwo$-sector. Moreover we find again necessary and sufficient conditions of
optimality of an abnormal trajectory for such systems, for any optimization
problem.
