论文标题
准连续动力系统的拓扑传递
Topological transitivity in quasi-continuous dynamical systems
论文作者
论文摘要
准连续的动力系统是由拓扑空间$ x $和映射$ f：x \ to x $组成的一对$（x，f）$，使得$ f^n $ is对于所有$ n \ in \ mathbb n $，在$ \ mathbb n $的情况下都是准n \ coasi comninuule。在本文中，我们表明，在适当的假设下，在准连续的动力系统中，拓扑传递概念的各种定义等效。我们的主要结果确定了准连续动力系统中拓扑和点传递性的等效性。这些扩展了[3]，[10]和[25]的连续动力学系统的一些经典结果，并在[7]和[8]中对准连续动态系统进行了一些结果。
A quasi-continuous dynamical system is a pair $(X,f)$ consisting of a topological space $X$ and a mapping $f: X\to X$ such that $f^n$ is quasi-continuous for all $n \in \mathbb N$, where $\mathbb N$ is the set of non-negative integers. In this paper, we show that under appropriate assumptions, various definitions of the concept of topological transitivity are equivalent in a quasi-continuous dynamical system. Our main results establish the equivalence of topological and point transitivity in a quasi-continuous dynamical system. These extend some classical results on continuous dynamical systems in [3], [10] and [25], and some results on quasi-continuous dynamical systems in [7] and [8].
