摘要
d-和d-跟踪性质是Dastjerdi和Hosseini为推广伪轨跟踪性质于2010年提出的.本文考察该动力性质在迭代系统和逆极限系统下的性质.首先证明对动力系统(X,f),以下三命题等价:(1)f具有d-跟踪性质(d-跟踪性质);(2)对任意k∈N,f^k也具有d-跟踪性质(d-跟踪性质);(3)存在k∈N,使得f^k具有d-跟踪性质(d-跟踪性质).进而证明具有d-跟踪性质的系统是链混合的.最后得到对于由{X_i,φ_i,f_i)_(i=1)~∞生成的逆极限系统(X_∞,f_∞),若每个f_i均具有d-跟踪性质(或者,d-跟踪性质,遍历跟踪性),则诱导映射f_∞也具有d-跟踪性质(相应地,d-跟踪性质,遍历跟踪性).
Abstract d- and d-shadowing properties were introduced by Dastjerdi and Hosseini in 2010 for generalizing the pseudo-orbit shadowing property. The aim of this paper is to investigate d- and d-shadowing properties of iteration systems and inverse limit systems. First, it is proved that for a dynamical system, the following three statements are equivalent： （1） f has d-shadowing property （resp., d-shadowing property）; （2） fk has d-shadowing property （resp., d-shadowing property） for all k∈ N; （3） fk has d-shadowing property （resp., d-shadowing property） for some k E N. Moreover, it is proved that a dynamical system having d-shadowing property is chain mixing. Finally, we obtain that the inverse limit system （X∞, f∞） generated by { i,φi, fi}i=1∞ has d-shadowing property （resp., d-shadowing property, ergodic shadowing property） provided that every fi has d-shadowing property （resp., d--shadowing property, ergodic shadowing property）.
出处
《中国科学：数学》
CSCD
北大核心
2015年第3期273-286,共14页
Scientia Sinica：Mathematica
基金
四川省教育厅基金(批准号:14ZB0007)
四川理工学院科研项目(批准号:2014RC02)资助项目
关键词
d-跟踪性质
链混合
逆极限系统
d-shadowing property, d-shadowing property, chain mixing, inverse limit system
