|
个人信息Personal Information
教授
博士生导师
硕士生导师
性别：男
毕业院校：复旦大学
学位：博士
所在单位：数学科学学院
学科：应用数学
办公地点：大连理工大学主校区科技园大厦A1124
联系方式：Tel:0411-84708351-8124
电子邮箱：fqli@dlut.edu.cn
Average Shadowing Property and Asymptotic Average Shadowing Property of Linear Dynamical Systems
点击次数：
论文类型：期刊论文
发表时间：2019-11-01
发表刊物：INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
收录刊物：EI、SCIE
卷号：29
期号：12
ISSN号：0218-1274
关键字：Average shadowing; asymptotic average shadowing; hyperbolicity
摘要：This paper investigates the average shadowing property and the asymptotic average shadowing property of linear dynamical systems in Banach spaces. Firstly, necessary and sufficient conditions for an invertible operator T on a Banach space to have the average shadowing property and the asymptotic average shadowing property are given, respectively. Then, it is concluded that both the average shadowing property and the asymptotic average shadowing property are preserved under iterations. Furthermore, if T is hyperbolic, then T has the (asymptotic) average shadowing property. However, the inverse implication fails in infinite-dimensional Banach spaces. Finally, it is proved that the (asymptotic) average shadowing property is equivalent to the hyperbolicity for dynamical systems in a finite-dimensional Banach space.