Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (1): 29-35.

• Articles • Previous Articles     Next Articles

The Complexity of Entropy-Minimal Dynamical Systems

 YIN Jian-Dong1, ZHOU Zuo-Ling2   

  1. 1. Department of Mathematics, Nanchang University, Nanchang |330031 2. Lingnan College, Zhongshan University, Guangzhou 510275
  • Online:2015-02-25 Published:2015-02-25

Abstract:

Let X be a compact metric space and f: XX  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 n1 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.

CLC Number: 

  • 37D45
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