  Work on standard piecewise-smooth (PWS) dynamical systems, with codimension-1
discontinuity sets, relies on the Filippov framework, which does not always
readily generalise to systems with higher codimension discontinuities. These
higher order degeneracies occur in applications, with spatial Coulomb friction
being the prominent example.
  In this work, we consider PWS systems with isolated codimension-2
discontinuity sets using regularization and blowup to study the dynamics. We
present a general framework and give specific results for the local dynamics in
a class of problems, and generalising Filippov sliding, crossing and sliding
vector fields.
