论文标题
平面不连续的分段差分系统的跨限制循环由等到中心形成
Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centers
论文作者
论文摘要
在过去的几年中，出现了越来越多的兴趣，研究了由丰富应用在建模真实现象中的不连续的分段差异系统。理解这些系统动态的困难之一是研究它们的极限周期。在本文中，我们研究了某些平面不连续的分段差异系统的交叉极限循环的最大数量，该系统由直线隔开，并通过线性中心（因此等于等级）和与均质非线性的线性中心（因此是等级等级中心的组合形成）形成。对于这些类别的平面不连续的分段差分系统，我们解决了第16个希尔伯特问题的扩展，即，我们为它们的最大交叉限制循环提供了上限。
These last years an increasing interest appeared for studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. One of the difficulties for understanding the dynamics of these systems is the study their limit cycles. In this paper we study the maximum number of crossing limit cycles of some classes of planar discontinuous piecewise differential systems separated by a straight line, and formed by combinations of linear centers (consequently isochronous) and cubic isochronous centers with homogeneous nonlinearities. For these classes of planar discontinuous piecewise differential systems we solved the extension of the 16th Hilbert problem, i.e. we provide an upper bound for their maximum number of crossing limit cycles.
