论文标题
在常规区域奇点和边界限制周期附近的非平滑差分系统的平滑系统平滑
Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles
论文作者
论文摘要
了解在平滑过程中切向奇异性是关于Filippov系统正规化的第一个问题之一。在本文中，我们对Filippov Systems的$ C^n $调查感兴趣，这些系统围绕可见的常规奇异性甚至多样化。更具体地说，使用Fenichel理论和爆炸方法，我们旨在了解正规化系统的轨迹如何通过正规化区域过渡。我们将结果应用于调查边界限制周期的$ C^n $调查，甚至与开关歧管接触甚至具有多重性接触。
Understanding how tangential singularities evolve under smoothing processes was one of the first problem concerning regularization of Filippov systems. In this paper, we are interested in $C^n$-regularizations of Filippov systems around visible regular-tangential singularities of even multiplicity. More specifically, using Fenichel Theory and Blow-up Methods, we aim to understand how the trajectories of the regularized system transits through the region of regularization. We apply our results to investigate $C^n$-regularizations of boundary limit cycles with even multiplicity contact with the switching manifold.
