  The sewed focus is one of the singularities of planar piecewise smooth
dynamical systems. Defined by Filippov in his book 'Differential Equations with
Discontinuous Righthand Sides' (Kluwer, 1988), it consists of two invisible
tangencies either side of the switching manifold. In the case of analytic
focus-like behaviour, Filippov showed that the approach to the singularity is
in infinite time. For the case of non-analytic focus-like behaviour, we show
that the approach to the singularity can be in finite time. For the
non-analytic sewed centre-focus, we show that there are uncountably many
different topological types of local dynamics, including cases with infinitely
many stable periodic orbits, and show how to create systems with periodic
orbits intersecting any bounded symmetric closed set.
