2025-12-302025-12-302025CARVALHO, Tiago; GONCALVES, Luiz Fernando; FREITAS, Bruno Rodrigues. Geometric singular perturbation on a positive measure minimal set of a planar piecewise smooth vector field. Nonlinear Analysis: hybrid systems, Amsterdam, v. 58, e101628, 2025. DOI: 10.1016/j.nahs.2025.101628. DisponÃvel em: https://www.sciencedirect.com/science/article/pii/S1751570X25000548. Acesso em: 8 dez. 2025.1751-570Xe- 1878-7460https://www.sciencedirect.com/science/article/pii/S1751570X25000548In this paper, we employ the geometric theory of singular perturbations to obtain detailed insights concerning a class of piecewise smooth vector fields exhibiting a positive measure minimal set. The canonical form used in our analysis represents a larger class of piecewise smooth systems, encompassing models of discontinuous harmonic oscillators. Through a desingularization process, which entails the application of a -regularization function along with successive weighted blow-ups (directional, spherical and polar), we obtain an attractor for the trajectories of the desingularized vector field .engAcesso RestritoDiscontinuous differential systemMinimal setSingular perturbationGeometric singular perturbation on a positive measure minimal set of a planar piecewise smooth vector fieldArtigo10.1016/j.nahs.2025.101628