Sensitivity of set-valued discrete systems

被引：30

作者：

Liu, Heng ^{[2
]}

Shi, Enhui ^{[1
]}

Liao, Gongfu ^{[3
,4
]}

机构：

[1] Suzhou Univ, Dept Math, Suzhou 215006, Jiangsu, Peoples R China

[2] Dalian Nationalities Univ, Dept Math, Dalian 116600, Liaoning, Peoples R China

[3] Jilin Normal Univ, Dept Math, Siping 136000, Jilin, Peoples R China

[4] Jilin Univ, Dept Math, Changchun 130012, Jilin, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 12期

关键词：

Set-valued mapping; Sensitivity; Path-connected space; CHAOS; TRANSITIVITY; HYPERSPACES; MAPPINGS; MAPS;

D O I：

10.1016/j.na.2009.06.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider the surjective, continuous map f : X -> X and the continuous map (f) over bar of X (X) into itself induced by f, where X is a compact metric space and X(X) is the space of all non-empty compact subsets of X endowed with a Hausdorff metric. In this paper we give examples showing that sensitivity off does not imply sensitivity of (f) over bar. Furthermore, we prove that if f is a surjective, continuous interval map, then (f) over bar is sensitive if and only if f is sensitive. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：6122 / 6125

页数：4

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