集值映射的伪轨跟踪和碎轨性质
首发时间:2019-04-08
摘要:本文研究了紧度量空间上集值映射的一些动力学性质。首先给出了集值映射的伪轨跟踪,平均伪轨跟踪的定义及其性质;并研究了非游荡点、链回归点的性质,证明了集值映射的非游荡点集与链回归点集在一定条件下是相等的;而且得到了集值映射在平均伪轨跟踪性质下的每一个点都是链回归点。其次本文还给出了集值映射的(局部)碎轨(specification)的定义,得到了碎轨性质与跟踪性的关系;并证明了满足拓扑混合的具有局部碎轨性质的集值映射具有正熵;还得到了集值映射具有碎轨性质的一个充分条件。
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Shadowing and Specification Properties for Set-valued Maps
Abstract:This paper studies the dynamical properties of the set-valued maps on compact distance space. This paper firstly gives the definition of shadowing and average-shadowing for set-valued maps and some properties of them, and investigates the properties of nonwondering points and chain recurrent points. Then the paper defines the specification for set-valued maps, and studies the relationship between specification of set-valued maps and shadowing. Furthermore, the paper proves that a set-valued map has positive entropy if it is topological mixing and has local specification property.
Keywords: Set-valued map Shadowing Specification Entropy
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