Geometric singular perturbartion theory for non-smooth dynamical systems
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In this article we deal with singularly perturbed Filippov systems Zε: (1) ˙x = ( F(x, y, ε) if h(x, y, ε) ≤ 0, G(x, y, ε) if h(x, y, ε) ≥ 0, εy˙ = H(x, y, ε), where ε ∈ R is a small parameter, x ∈ Rn, n ≥ 2, and y ∈ R denote the slow and fast variables, respectively, and F, G, h, and H are smooth maps. We study the effect of singular perturbations at typical singularities of Z0. Special attention will be dedicated to those points satisfying q ∈ {h(x, y, 0) = 0} ∩ {H(x, y, 0) = 0} where F or G is tangent to {h(x, y, 0) = 0}. The persistence and the stability properties of those objects are investigated.
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Publicacions Matemàtiques, v. EXTRA, p. 111-134, 2014.
