Resumen de On Piecewise Linear Differential Systems with n Limit Cycles of Arbitrary Multiplicities in Two Zones

Changwu Zou, Changjian Liu, Jiazhong Yang

• In this paper, we demonstrate rich dynamical phenomenon of piecewise linear differential systems having only two zones in the plane. We show that, for any given integer n and any integer tuple m=(m1,m2,⋯,mn), mi≥0, for i=1,⋯,n, there exists an aforementioned system which possesses exactly n limit cycles having multiplicities m1, m2,⋯,mn, respectively. (i.e. there are totally m1+m2+⋯+mn limit cycles taking into account of multiplicities). Moreover, we can even choose the separation boundary of the zones to be an algebraic curve.