The main goal of this paper is to present the existence of a vector field tangent to the unit sphere $ S^2 $ such that $ S^2 $ itself is a minimal set. This is reached using a piecewise smooth (discontinuous) vector field and following the Filippov's convention on the switching manifold. As a consequence, none regularization process applied to the initial model can be topologically equivalent to it and we obtain a vector field tangent to $ S^2 $ without equilibria.

中文翻译：

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不断流 \ begin {document} $ S ^ 2 $ \ end {document} 将球展示为最小设置

本文的主要目的是提出与单位球面$ S ^ 2 $相切的向量场的存在，使得$ S ^ 2 $本身是最小集。使用分段平滑（不连续）矢量场并遵循切换歧管上Filippov的约定来达到此目的。结果，应用于原始模型的任何正则化过程都无法在拓扑上等效于该模型，并且我们获得了与$ S ^ 2 $相切的向量场而没有平衡。