论文标题
分段光滑的全态系统
Piecewise Smooth Holomorphic Systems
论文作者
论文摘要
与全体形态系统相关的正常形式在文献中是众所周知的。在本文中，我们关心研究分段平滑的圆锥形系统（PWHS）。具体而言，我们从已知的正常形式和PWH的典型奇点对这些系统的可能相肖像进行了分类。此外，我们有兴趣了解与正规化区域的PWHS相关的正规化系统的轨迹。此外，我们知道尸体形态系统没有极限周期，但是分段平滑的全态系统可以，因此我们提供条件以确保存在这些系统的极限周期。提供其他条件以保证这种极限周期的稳定性和独特性。最后，我们给一些具有同质轨道的PWH家族。
The normal forms associated with holomorphic systems are well known in the literature. In this paper we are concerned about studying the piecewise smooth holomorphic systems (PWHS). Specifically, we classify the possible phase portraits of these systems from the known normal forms and the typical singularities of PWHS. Also, we are interested in understanding how the trajectories of the regularized system associated with the PWHS transits through the region of regularization. In addition, we know that holomorphic systems have no limit cycles, but piecewise smooth holomorphic systems do, so we provide conditions to ensure the existence of limit cycles of these systems. Additional conditions are provided to guarantee the stability and uniqueness of such limit cycles. Finally, we give some families of PWHS that have homoclinic orbits.
