The Limit Cycles of Discontinuous Piecewise Linear Differential Systems Formed by Centers and Separated by Irreducible Cubic Curves I

In the qualitative theory of the planar discontinuous piecewise linear differential systems one of the main problems is the study of the number of crossing limit cycles that these systems can have. We study the number of crossing limit cycles of discontinuous piecewise linear differential systems formed by centers and separated by an irreducible algebraic cubic curve. We prove that these differential systems only can exhibit 0, 1, 2 or 3 crossing limit cycles having two intersection points with the cubic of separation curve.