论文标题
$ \ mathbb {r}^{3} $中的分段平滑微分系统的不变歧管
Invariant manifolds for piecewise smooth differential systems in $\mathbb{R}^{3}$
论文作者
论文摘要
在本文中，考虑了三维差异系统的一些分段平滑扰动。在适当的原始差分系统的小扰动后，获得了周期轨道填充的不变歧管的存在。这些歧管从$ \ mathbb {r}^3 $的圆柱的连续体中出现，在某些平面代数多项式曲线旋转后，对于分段平滑的微分系统而言确实存在。用于获得结果的主要工具是分段平滑微分系统的平均理论。
In this paper some piecewise smooth perturbations of a three-dimensional differential system are considered. The existence of invariant manifolds filled by periodic orbits is obtained after suitable small perturbations of the original differential system. These manifolds emerge from a continuum of cylinders of $\mathbb{R}^3$ which does exist for the piecewise smooth differential systems after a rotation of some planar algebraic polynomial curves. The main tool used in order to obtain the results is the averaging theory for piecewise smooth differential systems.
