再论Devaney混沌的随机性质

Further Study on Stochastic Properties in Devaney's Chaos

拓扑动力系统相关动力性质(如弱混合、拓扑弱混合、敏感性)之间的关系一直是动力系统研究的主要问题。证明利用相关函数定义的弱混合拓扑动力系统必为拓扑弱混合。以此为基础,得到的系统是multi-敏感的和初值敏感依赖的。从而改进了相关文献的主要结果。

The relations among some dynamical properties （for example, weakly mixing, topologically and sensitivity） are main research for dynamical systems. It is proved that every weakly mixing dynamical weakly mixing, system defined using correlation function is topologically weakly mixing. Based on this result, it is obtained that such a system is multi-sensi- tive and sensitively dependent on initial conditions, improving the main results obtained by Wang Tao and Jia Nuo in 2010.