论文标题
二维流形的不连续矢量场的限制集
Limit sets of discontinuous vector fields on two-dimensional manifolds
论文作者
论文摘要
在本文中，研究了不连续矢量场轨迹的渐近行为。矢量场是在二维Riemannian歧管$ M $上定义的，并假定在某些合适的紧凑型套装$ k $ $ m $的轨迹上限制轨迹。全局轨迹的行为进行了充分的分析，并将其极限集分类。观察到具有非空内部的极限集的存在。此外，在$ M $上允许使用所谓的滑动运动。结果考虑了可能的限制集列表，以及非持续动力学的存在以及无确定性混乱的存在。本文还提供了一些拟合主要定理假设的系统的示例和类别。
In this paper the asymptotic behavior of trajectories of discontinuous vector fields is studied. The vector fields are defined on a two-dimensional Riemannian manifold $M$ and the confinement of trajectories on some suitable compact set $K$ of $M$ is assumed. The behavior of the global trajectories is fully analyzed and their limit sets are classified. The presence of limit sets having non-empty interior is observed. Moreover, the existence of the so called sliding motion is allowed on $M$. The results contemplate a list of possible limit sets as well the existence of non-recurrent dynamics and the presence of nondeterministic chaos. Some examples and classes of systems fitting the hypotheses of the main theorems are also provided in the paper.
