关于弱Specification性质的一个注记

Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (4): 601-606.

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)

Abstract

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

CLC Number:

O189.1

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

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A Remark on the Weak Specification Property

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