文献类型：期刊文献

中文题名：渐近跟踪性及其应用(英文)

英文题名：The Asymptotic Average Shadowing Property and Its Applications

作者：黎日松[1]

机构：[1]School of Science, Guangdong Ocean University

年份：2011

卷号：26

期号：4

起止页码：535

中文期刊名：数学季刊：英文版

外文期刊名：Chinese Quarterly Journal of Mathematics

收录：CSTPCD、、CSCD2011_2012、CSCD

基金：Supported by the NSF of Guangdong Province(10452408801004217);Supported by the Key Scientific and Technological Research Project of Science and Technology Department of Zhanjiang City(2010C3112005)

语种：中文

中文关键词：the POTP;the AASP;chain transitive;topologically transitive;topologically weakly mixing

外文关键词：the POTP the AASP chain transitive topologically transitive topologically weakly mixing

中文摘要：Let (X, d) be a bounded metric space and f : X → X be a uniformly continuous surjection. For a given dynamical system (X, f) which may not be compact, we investigate the relation between the asymptotic average shadowing property(AASP), transitivity and mixing. If f has the AASP, then the following statements hold: (1) f n is chain transitive for every positive integer n; (2) If X is compact and f is an expansive homeomorphism, then f is topologically weakly mixing; (3) If f is equicontinuous, then f is topologically weakly mixing; (4) If X is compact and f is equicontinuous, then f ×f is a minimal homeomorphism. We also show that the one-sided shift map has the AASP and the identity map 1 X does not have the AASP. Furthermore, as its applications, some examples are given.

外文摘要：Let （X, d） be a bounded metric space and f ： X → X be a uniformly continuous surjection. For a given dynamical system （X, f） which may not be compact, we investigate the relation between the asymptotic average shadowing property（AASP）, transitivity and mixing. If f has the AASP, then the following statements hold： （1） f n is chain transitive for every positive integer n; （2） If X is compact and f is an expansive homeomorphism, then f is topologically weakly mixing; （3） If f is equicontinuous, then f is topologically weakly mixing; （4） If X is compact and f is equicontinuous, then f ×f is a minimal homeomorphism. We also show that the one-sided shift map has the AASP and the identity map 1 X does not have the AASP. Furthermore, as its applications, some examples are given.