具有平均跟踪性质的连续半流  

Continuous semi-flows with the average-shadowing property

作　　者：王东明 牛应轩 WANG Dongming;NIU Yingxuan(School of Finance and Mathematics,West Anhui University,Lu’an 237012,China)

机构地区：[1]皖西学院金融与数学学院,安徽六安237012

出　　处：《安徽大学学报（自然科学版）》2019年第6期31-35,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61375121);安徽省高等学校自然科学研究重点项目(KJ2013A259).

摘　　要：设X是紧致度量空间,φ:■+×X→X是一个连续半流.讨论具有平均跟踪性质的连续半流与系统的动力性质的关系.证明具有平均跟踪性质且具有稠密的正半上密度回复点的连续半流φ是拓扑传递的,进一步地,如果连续半流φ具有平均跟踪性质且具有满支撑,则φ×φ是拓扑遍历的.Let X be a compact metric space and φ:■+×X→X be a continuous semi-flow. The relations between continuous semi-flows with the average-shadowing property and some dynamical properties are discussed. It is shown that if φ has the average shadowing property and the set of recurrent points with positive upper density of φ is dense in X , then φ is topologically transitive. Moreover, if φ has the average-shadowing property and full support, the φ×φ is topologically ergodic.

关 键 词：连续半流 拓扑传递 拓扑遍历 支撑 

分 类 号：O189.1[理学—数学]