论文标题
关于Devaney混乱的定义，用于连续的小组动作在Hausdorff统一空间上
On definition of Devaney chaos for a continuous group action on a Hausdorff uniform space
论文作者
论文摘要
我们表明，存在拓扑传递的非最低连续群体动作在Hausdorff统一空间上具有无限代理组的密集的周期点，并不一定意味着对此类系统中初始条件的敏感依赖性。这导致在Devaney的意义上定义混乱，以在原始方式上以无限代理的统一空间进行连续的小组动作，即具有密集的周期性点的非微不足道的拓扑和敏感系统，这是一个杂乱无章的系统。
We show that the existence of a dense set of periodic points for a topologically transitive non-minimal continuous group action on a Hausdorff uniform space with an infinite acting group does not necessarily imply a sensitive dependence to the initial conditions in such a system. This leads to define the chaos in the sense of Devaney for a continuous group action on a Hausdorff uniform spaces with an infinite acting group in the original way, i.e. a non-minimal topologically transitive and sensitive system with a dense set of periodic points is a chaotic system in the sense of Devaney.
