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This paper is concerned with the analysis of a typical singularity ofpiecewise smooth vector fields on $R^3$ composed by two zones. In our object ofstudy, the cusp-fold singularity, we consider the simultaneous occurrence of acusp singularity for one vector field and a fold singularity for the other one.We exhibit a normal form that presents one of the most important propertysearched for in piecewise smooth vector fields: the asymptotical stability.

An asymptotically stable cusp-fold singularity in 3D piecewise smooth vector fields