Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (5): 879-885.

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Some Remarks on P-Minimal Dynamical Systems

Wu Xinxing1, Wang Jianjun2   

  1. 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)

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

CLC Number: 

  • O189.1
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