关于P-极小动力系统的一些注记

数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 879-885.

关于P-极小动力系统的一些注记

吴新星¹, 王建军²

1. 西南石油大学理学院成都 610500;
2. 四川农业大学应用数学系四川雅安 625014

收稿日期:2015-12-07 修回日期:2016-06-18 出版日期:2016-10-26 发布日期:2016-10-26
作者简介:吴新星,E-mail:wuxinxing5201314@163.com;王建军,E-mail:wangjianjun02@163.com
基金资助:
西南石油大学科研起航计划项目（2015QHZ029）、四川省教育厅科学研究基金（14ZB0007）和国家自然科学基金（11401495，11601449）资助

Some Remarks on P-Minimal Dynamical Systems

Wu Xinxing¹, Wang Jianjun²

1. School of Sciences, Southwest Petroleum University, Chengdu 610500;
2. Department of Applied Mathematics, Sichuan Agricultural University, Sichuan Ya'an 625014

Received:2015-12-07 Revised:2016-06-18 Online:2016-10-26 Published:2016-10-26
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 (11401495, 11601449)

摘要/Abstract

摘要：

该文研究迭代系统和乘积系统的熵极小性与混沌极小性.首先证明熵极小动力系统要么是syndetic-敏感的，要么是极小等度连续的.其次，得到对任意自然数n≥2，存在熵极小和混沌极小的动力系统，满足其n-次迭代系统既不是熵极小的也不是混沌极小的.同时，证明如果乘积系统是熵极小，则每个因子系统都是熵极小的；但是其逆不真.

关键词: 熵极小, 混沌极小, 迭代系统, 乘积系统

Abstract:

This paper is devoted to the study of entropy-minimality and chaos-minimality of iteration systems and product systems. Firstly, we prove that an entropy-minimal system is either syndetically sensitive or minimal and equicontinuous. Then, we obtain that for each positive integer n≥2, there is an entropy-minimal and chaos-minimal system such that its n-th iteration system is neither entropy-minimal nor chaos-minimal. Besides, we show that each factor system is entropy-minimal provided that the product system is entropy-minimal, and its converse is not true.

Key words: Entropy-minimality, Chaos-minimality, Iteration system, Product system

中图分类号:

O189.1

吴新星, 王建军. 关于P-极小动力系统的一些注记[J]. 数学物理学报, 2016, 36(5): 879-885.

Wu Xinxing, Wang Jianjun. Some Remarks on P-Minimal Dynamical Systems[J]. Acta mathematica scientia,Series A, 2016, 36(5): 879-885.

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