Peixoto's Theorem for vector fields on S2 with impasse points - Buzzi, Claudio A. [UNESP]; da Silva, Paulo R. [UNESP]; Medrado, João C.R. (Elsevier, 2013)
The structural stability of vector fields with impasse regular curves on S2 is studied and a version of Peixoto's Theorem is established. Moreover a global analysis of normal forms of the constrained systems. A(x).ẋ=F(x),x∈R3,A∈M(3),F:R3→R3 in the Poincaré ball (i.e. in the compactification of R3 with the sphere S2 of the infinity) is made. © 2013 Elsevier Masson SAS.
Keywords: Constrained systems; Discontinuous vector fields; Regularization; Singular perturbation; Sliding vector fields; Vector fields