Generic bifurcation of sliding vector fields (Q1260877)

The author classifies the codimension 1 singularities which generically occur in one-parameter families of sliding vector fields arising from differential equations on \(\mathbb{R}^ 3\) with discontinuous right-hand side. In the paper is assumed that these discontinuities appear on the 2- sphere \(S^ 2\) and the solution orbits of the ordinary differential equation on \(S^ 2\) are defined using Filippov's convention [see \textit{A. F. Filippov}, Differential equations with discontinuous right-hand sides, Dordrecht (1988; Zbl 0664.34001)] where some physical models are presented to illustrate the interest of this kind of problems.