Several Transitive Properties and Devaney's Chaos  

作　　者：Tao WANG Jian Dong YIN Qi YAN 

机构地区：[1]Department of Mathematics,Nanchang University

出　　处：《Acta Mathematica Sinica,English Series》2016年第3期373-383,共11页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11261039);National Natural Science Foundation of Jiangxi Province(Grant No.20132BAB201009)

摘　　要：The relation among transitivity, indecomposability and Z-transitivity is discussed. It is shown that for a non-wandering system （each point is non-wandering）, indecomposability is equivalent to transitivity, and for the dynamical systems without isolated points, Z-transitivity and transitivity are equivalent. Besides, a new transitive level as weak transitivity is introduced and some equivalent conditions of Devaney＇s chaos are given by weak transitivity. Moreover, it is proved that both d- shadowing property and d-shadowing property imply weak transitivity.The relation among transitivity, indecomposability and Z-transitivity is discussed. It is shown that for a non-wandering system （each point is non-wandering）, indecomposability is equivalent to transitivity, and for the dynamical systems without isolated points, Z-transitivity and transitivity are equivalent. Besides, a new transitive level as weak transitivity is introduced and some equivalent conditions of Devaney＇s chaos are given by weak transitivity. Moreover, it is proved that both d- shadowing property and d-shadowing property imply weak transitivity.

关 键 词：Devaney＇s chaos INDECOMPOSABILITY Z-transitivity weak transitivity 

分 类 号：O19[理学—数学] O415.5[理学—基础数学]