论文标题
来自中心形成的周期性环和两个鞍座的限制周期的分叉，在分段线性差分系统中，带有三个区域
Bifurcation of Limit Cycles from a Periodic Annulus Formed by a Center and Two Saddles in Piecewise Linear Differential System with Three Zones
论文作者
论文摘要
在本文中，我们研究了可以从不连续的平面分段线性线性汉密尔顿差速器系统中分叉的极限循环的数量，该循环量具有三个平行直线的三个区域，因此定义分段的线性差速器系统具有一个中心和两个鞍座。也就是说，两个平行线（即中央子系统）之间的区域中的线性差分系统具有中心，而其他子系统具有鞍座。我们证明，如果中央子系统具有真实或边界中心，那么我们至少有六个限制循环通过线性扰动从周期性的环上分叉，四个通过三个区域和两个通过两个区域。现在，如果中央子系统具有虚拟中心，那么我们至少有四个极限周期通过线性扰动从周期性的环上分叉，三个通过三个区域，一个通过两个区域。为此，我们获得了这些分段哈密顿系统的正常形式，并研究了其在两个区域和三个区域中定义的墨尼科夫函数的零数
In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines, such that the linear differential systems that define the piecewise one have a center and two saddles. That is, the linear differential system in the region between the two parallel lines (i.e. the central subsystem) has a center and the others subsystems have saddles. We prove that if the central subsystem has a real or a boundary center, then we have at least six limit cycles bifurcating from the periodic annulus by linear perturbations, four passing through the three zones and two passing through the two zones. Now, if the central subsystem has a virtual center, then we have at least four limit cycles bifurcating from the periodic annulus by linear perturbations, three passing through the three zones and one passing through the two zones. For this, we obtain a normal form for these piecewise Hamiltonian systems and study the number of zeros of its Melnikov functions defined in two and three zones
