论文标题
关于不连续的分段线性近距离山米尔顿差分系统的环循环性，三个区域在中央一个
On cyclicity in discontinuous piecewise linear near-Hamiltonian differential systems with three zones having a saddle in the central one
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线性汉密尔顿差分系统的周期性环上分叉的极限周期数量，三个区域与两个平行的直线分隔，以使得在两个直线之间由零件（召集了中央系数）之间的区域中的一个线性差异系统（在一个零件中）给出了这些零件（称为“平均数为sopiss of Chinces of Chentrys”）。马鞍和中心）。我们证明，通过线性扰动，这种分段汉密尔顿差异系统的周期性周期性的分叉的最大限制循环数量至少为六个。为此，我们获得了系统的正常形式，并研究了其在两个区域和三个区域中定义的Melnikov功能的零数。
In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus of discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines, such that the linear differential system, given by the piecewise one, in the region between the two straight lines (called of central subsystem) has a saddle at a point equidistant from these lines (obviously, the others subsystems have saddles and centers). We prove that the maximum number of limit cycles that bifurcate from the periodic annulus of this kind of piecewise Hamiltonian differential systems, by linear perturbations, is at least six. For this, we obtain normal forms for the systems and study the number of zeros of its Melnikov functions defined in two and three zones.
