拓 扑 链 遍 历 映 射

拓扑链遍历映射

孟鑫¹, 关志强², 刘国清³

1. 吉林师范大学数学学院，吉林四平 136000； 2. 沈阳大学新民师范学院, 沈阳 110300； 3. 大庆师范学院数学系, 黑龙江大庆 163712

收稿日期:2007-08-28 修回日期:1900-01-01 出版日期:2008-05-26 发布日期:2008-05-26
通讯作者: 关志强

Mapping of Topological Chain Ergodicity

MENG Xin¹, GUAN Zhiqiang², LIU Guoqing³

1. College of Mathematics, Jilin Normal University, Siping 136000, Jilin Province, China;\=2. Xinmin Teachers’ College, Shenyang University, Shenyang 110300, China；3. Department of Mathematics, Daqing Teachers’ College, Daqing 163712, Heilongjiang Province, China

Received:2007-08-28 Revised:1900-01-01 Online:2008-05-26 Published:2008-05-26
Contact: GUAN Zhiqiang

摘要/Abstract

摘要： 通过引进链遍历的概念以及链遍历与拓扑遍历的关系, 证明了拓扑遍历蕴涵链遍历但反之不然, 指出对于满足伪轨跟踪性质的映射两种性质是等价的, 并给出了动力系统序列与其生成的逆极限系统之间链遍历的相互蕴涵性, 推广了拓扑遍历性已有的相应结果.

关键词: 链遍历, 拓扑遍历, 逆极限空间

Abstract: By introducing the definition of chain ergodicity and its relationship with topological ergodicity, this paper proves that if topological ergodicity is fulfilled, the chain ergodicity will be fulfilled, too, while it’s not true conversely. Further, it is pointed out that the two properties of mapping which meet the demand of pseudoorbit tracing properties are equivalent. In addition, the present paper presents that if the power system squence is fulfilled, its generated converse limit system will be fulfilled, too, and it’s also true conversely and hence develops the corresponding theory of topological ergodicity.

Key words: chain ergodicity, topological ergodicity, converse limit space

中图分类号:

O189.1

孟鑫, 关志强, 刘国清. 拓扑链遍历映射[J]. J4, 2008, 46(03): 475-477.

MENG Xin, GUAN Zhiqiang, LIU Guoqing. Mapping of Topological Chain Ergodicity[J]. J4, 2008, 46(03): 475-477.