Crossing limit cycles for a class of piecewise linear differential centers separated by a conic

Abstract

In previous years the study of the version of Hilbert's 16th problem for piecewise linear differential systems in the plane has increased. There are many papers studying the maximum number of crossing limit cycles when the differential system is defined in two zones separated by a straight line. In particular in [11, 13] it was proved that piecewise linear differential centers separated by a straight line have no crossing limit cycles. However in [14, 15] it was shown that the maximum number of crossing limit cycles of piecewise linear differential centers can change depending of the shape of the discontinuity curve. In this work we study the maximum number of crossing limit cycles of piecewise linear differential centers separated by a conic.