On homeomorphisms with the two-sided limit shadowing property
On homeomorphisms with the two-sided limit shadowing property
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具有两侧极限阴影性质的同胚
DOI：
10.1016/j.jmaa.2014.06.011
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发表时间：
2014
影响因子：
1.3
通讯作者：
Dominik Kwietniak
中科院分区：
文献类型：
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作者：
B. Carvalho;Dominik Kwietniak
我们证明了双边极限跟踪属性是最强的伪轨道跟踪已知的概念之一。它包含跟踪、平均跟踪、渐近平均跟踪和规范性质。我们还引入了一个较弱的概念，称为双边极限跟踪与间隙，并证明它意味着跟踪和传递性。我们证明，这两个性质允许描述一类扩展同胚中的拓扑传递性和混合性，因此它们描述了有限类型的传递（混合）移位。
We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a weaker notion that is called two-sided limit shadowing with a gap and prove that it implies shadowing and transitivity. We show that those two properties allow to characterize topological transitivity and mixing in a class of expansive homeomorphisms and hence they characterize transitive (mixing) shifts of finite type.