Two-fold singularities in nonsmooth dynamics-Higher dimensional analogs.

When a system of ordinary differential equations is discontinuous along some threshold, its flow may become tangent to that threshold from one side or the other, creating a fold singularity, or from both sides simultaneously, creating a two-fold singularity. The classic two-fold exhibits intricate local dynamics and accumulating sequences of local bifurcations and is by now rather well understood, but it is just the simplest of an infinite hierarchy of two-folds and multi-folds in higher dimensions. These arise when a system is discontinuous along multiple intersecting thresholds, and the induced sliding flows on those thresholds become tangent to their intersections.