An Update on that Singularity
It took nearly 30 years from the translation of Filippov’s seminal book to be able to say that the two-fold singularity is understood. We now know that its structural stability requires nonlinear switching or hidden terms, and that it comes in three main flavours, with numerous subclasses between which bifurcations can occur. We know that it is neither an attractor nor a repellor, but a bridge between attracting and repelling sliding and, in certain cases, is a source of determinacy-breaking.
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