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Geometric singular perturbation theory for non-smooth dynamical systems. (English) Zbl 1323.34021

From the closing remarks: “Non-smooth singularly perturbed systems are studied in this paper. We investigate the effect of singular perturbations at tangency points. We prove that singularities of the type fold are robust with respect to singular perturbations. On the other hand, cusp singularities are not robust with respect to singular perturbations. We also study the unfolding of cusp singularities and hyperbolic equilibria.”

MSC:

34A36 Discontinuous ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34C26 Relaxation oscillations for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
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