论文标题
打结的环形套件，吸引子和不可压缩的表面
Knotted toroidal sets, attractors and incompressible surfaces
论文作者
论文摘要
在本文中，我们对那些打结的环形组进行了完整的表征，这些集合可以作为$ \ mathbb {r}^3 $全球定义的离散和连续动态系统的吸引子。我们还看到，用于解决此问题的技术可用于提供足够的条件，以确保$ \ mathbb {r}^3 $的一类巨大的子曲系是同构的吸引子，也必须吸引流量。此外，我们研究了$ \ mathbb {s}^3 $的某些吸引者练习器分解，这些分解自然会在考虑环形组合时出现。
In this paper we give a complete characterization of those knotted toroidal sets that can be realized as attractors for both discrete and continuous dynamical systems globally defined in $\mathbb{R}^3$. We also see that the techniques used to solve this problem can be used to give sufficient conditions to ensure that a wide class of subcompacta of $\mathbb{R}^3$ that are attractors for homeomorphisms must also be attractors for flows. In addition we study certain attractor-repeller decompositions of $\mathbb{S}^3$ which arise naturally when considering toroidal sets.
