关于弱Specification性质的一个注记

数学物理学报 ›› 2017, Vol. 37 ›› Issue (4): 601-606.

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关于弱Specification性质的一个注记

吴新星^1,2

1 西南石油大学理学院成都 610500;
2 西南石油大学非线性动力系统研究所成都 610500

收稿日期:2016-08-20 修回日期:2017-01-21 出版日期:2017-08-26 发布日期:2017-08-26
作者简介:吴新星,E-mail:wuxinxing5201314@163.com
基金资助:
西南石油大学科研起航计划（2015QHZ029）、四川省教育厅科学研究基金（14ZB0007）和国家自然科学基金

A Remark on the Weak Specification Property

Wu Xinxing^1,2

1 School of Sciences, Southwest Petroleum University, Chengdu 610500;
2 Institute of Nonlinear Dynamics, Southwest Petroleum University, Chengdu 610500

Received:2016-08-20 Revised:2017-01-21 Online:2017-08-26 Published:2017-08-26
Supported by:
Supported by the Scientific Research Starting Project of Southwest Petroleum University (2015QHZ029), the Scientific Research Fund of the Sichuan Provincial Education Department (14ZB0007) and the NSFC (11601449)

摘要/Abstract

摘要： 该文证明具有弱specification性质的系统在其测度中心的限制系统也具有弱specification性质，并且其逆不真.作为推论得到在未有满射的假设下，弱specification性质蕴含渐近平均跟踪性质.最后证明具有弱specification性质的满射系统是一致分布混沌的.

关键词: 测度中心, 弱specification, 渐近平均跟踪性质, 分布混沌

Abstract: This note proves that if a dynamical system has the weak specification property, then so does the dynamical system restricted on its measure center, and the converse does not hold. As a corollary, it is obtained that the weak specification property implies asymptotic average shadowing (no assumption that the map is onto). Finally, it is proved that every surjective system having the weak specification property exhibits uniformly distributional chaos.

Key words: Measure center, Weak-specification, Asymptotic average shadowing, Distributional chaos

中图分类号:

O189.1

吴新星. 关于弱Specification性质的一个注记[J]. 数学物理学报, 2017, 37(4): 601-606.

Wu Xinxing. A Remark on the Weak Specification Property[J]. Acta mathematica scientia,Series A, 2017, 37(4): 601-606.

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关于弱Specification性质的一个注记

A Remark on the Weak Specification Property

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