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In this paper we study the Sotomayor-Teixeira regularization of a generalvisible fold singularity of a Filippov system. Extending Geometric FenichelTheory beyond the fold with asymptotic methods, we determine there thedeviation of the orbits of the regularized system from the generalizedsolutions of the Filippov one. This result is applied to the regularization ofsome global sliding bifurcations as the Grazing-Sliding of periodic orbits orthe Sliding Homoclinic to a Saddle, as well as to some classical problems indry friction. Roughly speaking, we see that locally, and also globally, theregularization of the bifurcations preserve the topological features of thesliding ones.

Regularization of sliding global bifurcations derived from the local fold singularity of Filippov systems