作　　者： ;

机构地区： 广东海洋大学理学院

出　　处： 《太原理工大学学报》 2007年第3期278-282,共5页

摘　　要： 设(X,d)是紧致度量空间,f:X→X是连续的,n为任一给定的正整数,证明了:f是链可迁的当且仅当fn是链可迁的;若同胚f是Lipschitz映射,则f有平均跟踪性当且仅当fn有平均跟踪性。设f是个同胚映射,得到了如下结果:若f有POTP且是distal的,则fn不具有平均跟踪性;若f有平均跟踪性且是等度连续的,则fn是极小的;若f是distal的且是链可迁的,则fn不具有POTP;f是distal的当且仅当fn是distal的。同时,还给出了例子:设S={0,1,…,k-1},σ∶∑(S)→∑(S)(resp.σ∶∑+(S)→∑+(S))为符号空间上的移位自映射,则nσ(resp.nσ+)有平均跟踪性. Let （X,d） be a compact metric space and f：X→X be continuous. And let n be a given positive integer. In this paper,the following statements were proved： f is chaintransitive if and only if f^n is chaintransitive;if a homeomorphismf is a Lipschitz map,then f has the average shadowing property if and only if f^n has the average shadowing property. Let f be a homeomorphism,the following statements were obtained, if f is distal and has POTP,then f^n does not have the average shadowing property;if f is equicontinuous and has the average shadowing property, then f^n is minimal; let f： X→X be distal and chaintransitive, then f^n does not have POTP; f is distal if and only if f^n is distal. At the same time, the following example was given： Let σ：∑（S） → （S）（resp.）σ： ∑＋ （S）→∑＋ （S）） be the shift map on the symbolic space and S={0,1,…, k- 1}. then σ（resp, σ＋ ） has the average shadowing property if and only if σ^n （resp. σ＋^n ） has the average shadowing property.

关 键 词： 平均跟踪 伪轨跟踪 极限跟踪 跟踪 链可迁 同胚

领　　域： [理学] [理学]