Attractors of Local Semiflows on Topplogical Spaces
Attractors of Local Semiflows on Topplogical Spaces
复制标题
拓扑逻辑空间上局部半流的吸引子
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Youbing Xiong
中科院分区：
文献类型：
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作者：
Desheng Li;Jintao Wang;Youbing Xiong
本文引入拓扑空间上局部半流吸引子的概念，在某些情况下，它似乎比文献中已有的吸引子更合适。基于这一概念，我们发展了一个基本的吸引子理论的拓扑空间下适当的分离公理。首先，我们讨论吸引子的基本性质，如极大性和稳定性，并建立一些存在性结果。然后，我们给出了一个匡威李雅普诺夫定理。最后，还讨论了吸引子的莫尔斯分解。
In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.