熵极小动力系统的复杂性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (1): 29-35.

熵极小动力系统的复杂性

尹建东¹, 周作领²

1. 南昌大学数学系南昌 330031 2. 中山大学岭南学院广州 510275

出版日期:2015-02-25 发布日期:2015-02-25
基金资助:
国家自然科学基金(11261039, 11371379)、国家自然科学天元基金(11326099)和江西省自然科学基金(20132BAB201009)资助

The Complexity of Entropy-Minimal Dynamical Systems

YIN Jian-Dong¹, ZHOU Zuo-Ling²

1. Department of Mathematics, Nanchang University, Nanchang |330031 2. Lingnan College, Zhongshan University, Guangzhou 510275

Online:2015-02-25 Published:2015-02-25

摘要/Abstract

摘要：

设X是一个紧致度量空间, f: X $\100dpi \inline \rightarrow$ X 是一个连续映射, (X,f)是熵极小的. 该文首先证明了f是强遍历的;另外, 如果还假设X中存在f的一个真的(拟)弱几乎周期点, 则得到 f 具有正拓扑熵且对任意的n $\100dpi \inline \geq$ 1, fⁿ 是遍历敏感依赖的. 因此,f 在Li-Yorke 和 Takens-Ruelle意义下是混沌的.该文所得结论改进和推广了最近的一些结论.

关键词: 熵极小 , 强遍历 , 遍历敏感依赖 , 拓扑熵

Abstract:

Let X be a compact metric space and f: X $\100dpi \inline \rightarrow$ X be a continuous map. In this paper, we prove that f is strongly ergodic if f is entropy-minimal.In addition, we show that f has positive topological entropy and fⁿ is ergodically sensitive for any n $\100dpi \inline \geq$ 1 if there exists a proper (quasi) weakly almost periodic point of f , hence f is chaotic in the sense of Li-Yorke and Takens-Ruelle.The presented results improve and generalize some recent results.

中图分类号:

37D45

尹建东, 周作领. 熵极小动力系统的复杂性[J]. 数学物理学报, 2015, 35(1): 29-35.

YIN Jian-Dong, ZHOU Zuo-Ling. The Complexity of Entropy-Minimal Dynamical Systems[J]. Acta mathematica scientia,Series A, 2015, 35(1): 29-35.