A Behavioral Characterization of Discrete Time Dynamical Systems over Directed Graphs

被引：2

作者：

Ackerman, Jonathan ^{[1
]}

Ayers, Kimberly ^{[1
]}

Beltran, Eduardo J. ^{[2
]}

Bonet, Joshua ^{[2
]}

Lu, Devin ^{[3
]}

Rudelius, Thomas ^{[4
]}

机构：

[1] Bowdoin Coll, Dept Math, Brunswick, ME 04011 USA

[2] Univ Puerto Rico, Dept Math, Rio Piedras, PR 00931 USA

[3] Stanford Univ, Dept Math, Stanford, CA 94309 USA

[4] Cornell Univ, Dept Math, Ithaca, NY 14850 USA

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2014年 / 13卷 / 01期

基金：

美国国家科学基金会;

关键词：

Morse Decomposition; Morse Sets; Shift Space; Symbolic Dynamical System; Recurrent Chain;

D O I：

10.1007/s12346-014-0111-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using a directed graph, a Markov chain can be treated as a dynamical system over a compact space of bi-infinite sequences, with a flow given by the left shift of a sequence. In this paper, we show that the Morse sets of the finest Morse decomposition on this space can be related to communicating classes of the directed graph by considering lifting the communicating classes to the shift space. Finally, we prove that the flow restricted to these Morse sets is chaotic.

引用

页码：161 / 180

页数：20

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