Closing Lemma for piecewise smooth vector fields with a recurrent point - Antunes, A. A. [UNESP]; Carvalho, T.; Gomide, O. M.L. (Elsevier, 2024)
In this paper we provide a positive answer for the C0-Closing Lemma in the context of n-dimensional piecewise smooth vector fields governed by the Filippov's rules. So, given a model presenting a nontrivially recurrent point it is possible to consider a C0-close perturbation of it possessing a closed trajectory. Also, we conclude the paper proving the existence of a closed orbit around a T-singularity.
Keywords: Closing lemma; Piecewise smooth vector field; Recurrence