Abstract
ABSTRACTIn this work, we consider piecewise smooth vector fields X defined in , where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields , satisfying that converges uniformly to X in each compact subset of when . We define the sliding region on the non-regular part of Σ as a limit of invariant manifolds of . Since the double regularization provides a slow–fast system, the GSP-theory (geometric singular perturbation theory) is our main tool.
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