Singular impasse points of planar constrained differential systems

Abstract

Planar analytic constrained differential systems (or impasse systems) are given by (Formular Presented) where F is a vector field and A is a matrix valued function. This class of systems differs from classical ODE’s due to existence of the so called impasse set ∆ = {x : det A(x) = 0}. The dynamics near smooth impasse points is well known in the literature (see for instance [17, 28, 31]). In this paper, we use Newton polygon and weighted blow ups in order to study its phase portrait near singular points of ∆. Moreover, we apply our results in electric circuit problems.