Dynamics of induced systems
Dynamics of induced systems
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DOI：
10.1017/etds.2016.7
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发表时间：
2014-12
影响因子：
0.9
通讯作者：
E. Akin;J. Auslander;Anima Nagar
中科院分区：
文献类型：
--
作者：
E. Akin;J. Auslander;Anima Nagar
本文研究了相空间紧子集空间上作用的动力学性质。更准确地说，如果$X$是一个度量空间，设$2^{X}$表示具有Hausdorff拓扑的$X$的非空紧子集的空间。如果$f$是$X$上的连续自映射，则在$2^{X}$上存在一个自然导出的连续自映射$f_{\ast}$。我们的主题是$f$和$f_{\ast}$的动态之间的相互关系。对于这样的研究，考虑具有一致收敛拓扑的康托尔集$K$到$X$的连续映射的空间${\mathcal{C}}(K，X)$，以及在${\mathcal{C}}(K，X)$上通过组合映射导出的$f_{\ast}$是有用的。本文主要从拓扑和动态两个方面研究了归纳系统$(2^{X},f_{\ast})$的传递点的性质，并给出了一些例子。我们还研究了系统$(2^{X},f_{\ast})$的更多属性。
In this paper we study the dynamical properties of actions on the space of compact subsets of the phase space. More precisely, if $X$ is a metric space, let $2^{X}$ denote the space of non-empty compact subsets of $X$ provided with the Hausdorff topology. If $f$ is a continuous self-map on $X$ , there is a naturally induced continuous self-map $f_{\ast }$ on $2^{X}$ . Our main theme is the interrelation between the dynamics of $f$ and $f_{\ast }$ . For such a study, it is useful to consider the space ${\mathcal{C}}(K,X)$ of continuous maps from a Cantor set $K$ to $X$ provided with the topology of uniform convergence, and $f_{\ast }$ induced on ${\mathcal{C}}(K,X)$ by composition of maps. We mainly study the properties of transitive points of the induced system $(2^{X},f_{\ast })$ both topologically and dynamically, and give some examples. We also look into some more properties of the system $(2^{X},f_{\ast })$ .