以环面或球面为滑动流形的非光滑向量场
On non-smooth vector fields having a torus or a sphere as the sliding manifold
摘要：
本文考虑非光滑向量场$Z=(X,Y)$，其中$X,Y$是三维线性向量场，$Z$的不连续流形$Σ$是通常的嵌入环面或原点酉球面.通过考虑$Σ$上的$X,Y$是非弹性的，我们假设$Σ$是一个带切线的滑动（稳定/不稳定）流形.在每一种情况下，我们研究了向量场$Z$与$Σ$的相切，并描述了在$Σ$上滑动向量场的轨迹的行为：它们基本上是封闭的。
英文摘要：
In this paper we consider a non-smooth vector field $Z=(X,Y)$, where $X,Y$ are linear vector fields in dimension 3 and the discontinuity manifold $Σ$ of $Z$ is or the usual embedded torus or the unitary sphere at origin. We suppose that $Σ$ is a sliding (stable/unstable) manifold with tangencies, by considering $X,Y$ inelastic over $Σ$. In each case, we study the tangencies of the vector field $Z$ with $Σ$ and describe the behavior of the trajectories of the sliding vector field over $Σ$: they are basically closed.
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