2017/06/22 by Daniel Panazzolo, Paulo Ricardo da Silva
Mathematics · #Advanced Differential Equations and Dynamical Systems #Computer science #Discontinuity (linguistics) #Foliation (geology) #Geometric Analysis and Curvature Flows #Locus (genetics) #Manifold (fluid mechanics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #Regularization (linguistics) #Sigma #math.DS #msc:34C45 #sort
paper · pdf · doi:10.1016/j.jde.2017.08.042
32 pages
arxiv created 2017/06/22 · openalex publication_date 2017/09/07 · arxiv updated 2017/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the regularization of an oriented 1-foliation F on M ∖ Σ where M is a smooth manifold and Σ⊂ M is a closed subset, which can be interpreted as the discontinuity locus of F. In the spirit of Filippov's work, we define a sliding and sewing dynamics on the discontinuity locus Σ as some sort of limit of the dynamics of a nearby smooth 1-foliation and obtain conditions to identify whether a point belongs to the sliding or sewing regions.