Devaney定义下变换的拓扑和随机性质的关系

Links between topological and stochastic properties of transformation in definition of Devaney′s chaos

利用拓扑和遍历理论对Devaney混沌意义下变换的弱混合与拓扑混合、拓扑传递及初值敏感的关系进行了研究,改进了已有文献的结论,证明了弱混合则初值敏感.

We explored the relationships between topological mixing and weak mixing, weak mixing and topological transitivity, weak mixing and sensitive dependence on initial conditions in the sense of Devaney＇s chaos by using topology and ergodic theory. The main result that weak mixing can be seen as a new sufficient condition to sensitive dependence on initial conditions is obtained, which improves the results in existing literature