Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces
Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces
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非紧且不可度量空间上的拓扑阿诺索夫同胚的谱分解
DOI：
10.1016/j.topol.2012.10.010
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发表时间：
2011
影响因子：
0.6
通讯作者：
J. Wiseman
中科院分区：
文献类型：
--
作者：
T. Das;Keonhee Lee;David Richeson;J. Wiseman
我们讨论了同胚的扩张性，跟踪和链递归的拓扑定义。它们推广了度量空间的通常定义。我们证明了各种定理拓扑Anosov同胚（地图是膨胀的，并有跟踪属性）的非紧和非度量空间，推广定理，这样的同胚紧度量空间。主要结果是将Smale的谱分解定理推广到第一可数、局部紧、仿紧、Hausdorff空间上的拓扑Anosov同胚。
We discuss topological definitions of expansivity, shadowing, and chain recurrence for homeomorphisms. They generalize the usual definitions for metric spaces. We prove various theorems about topologically Anosov homeomorphisms (maps that are expansive and have the shadowing property) on noncompact and non-metrizable spaces that generalize theorems for such homeomorphisms on compact metric spaces. The main result is a generalization of Smaleʼs spectral decomposition theorem to topologically Anosov homeomorphisms on first countable, locally compact, paracompact, Hausdorff spaces.