Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line

Abstract

In this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain again at least five limit cycles but now from infinity, which is of monodromic type, and with simpler computations. The proof uses a partial classification of the center problem when both systems are of center type.