动力系统通过外空间的极限和端函子
Limit and end functors of dynamical systems via exterior spaces
摘要：
本文分析了外空间范畴在动力系统（流）研究中的一些应用。我们研究了动力系统的吸收开子集的概念，即，包含所有轨迹的“未来部分”的开子集。所有吸收开子集的族是一个拟滤子，它给出了流的外部空间的结构。利用外空间的极限空间和端空间构造动力系统的极限空间和端空间。一方面，构造了动力系统的两个极限空间$L^{\r}(X)$和$\bar L^{\r}(X)$，并分析了它们与周期、Poisson稳定点的子流以及$X$的$Ω^{\r}$ -极限的关系.另一方面，不同的端空间也与一个动力系统相关联，该动力系统具有任何正半轨线在这些端空间中都有端点的性质。这种类型的构造允许我们考虑包含在终点$a$结束的所有轨迹的子流。当$a$运行在所有端点的集合上时，我们将动力系统诱导分解为稳定（在无穷远处）子流的不相交并集。
英文摘要：
In this paper we analyze some applications of the category of exterior spaces to the study of dynamical systems (flows). We study the notion of an absorbing open subset of a dynamical system; i.e., an open subset that contains the "future part" of all the trajectories. The family of all absorbing open subsets is a quasi-filter which gives the structure of an exterior space to the flow. The limit space and end space of an exterior space is used to construct the limit spaces and end spaces of a dynamical system. On the one hand, for a dynamical system two limits spaces $L^{\r}(X)$ and $\bar L^{\r}(X)$ are constructed and their relations with the subflows of periodic, Poisson stable points and $Ω^{\r}$-limits of $X$ are analyzed. On the other hand, different end spaces are also associated to a dynamical system having the property that any positive semi-trajectory has an end point in these end spaces. This type of construction permits us to consider the subflow containing all trajectories finishing at an end point $a$. When $a$ runs over the set of all end points, we have an induced decomposition of a dynamical system as a disjoint union of stable (at infinity) subflows.
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