【摘要】 从系统的回复性质、不可分解性和复杂性等方面讨论了两个符号半动力系统的乘积系统的动力学性质。具体结果如下:(1)该系统有以任何正整数n为周期的周期点,并且周期点集在∑+m×∑+m中稠密;(2)通过构造一个轨道在∑+m×∑+m中稠密的点,证明了该系统的拓扑传递性;(3)该系统是拓扑混合的;(4)借助于对该系统正向可扩性的讨论,得到了该系统在Devaney意义下混沌的结论。更多还原

【Abstract】 This paper discusses dynamical properties of the product of two symbolic semi-dynamical systems in the respects of the system’s recurrence,indecomposability and complexity. The results are as follows:( 1) for every positive integer n,the system has a periodic point with period n;( 2) by constructing a point whose orbit is dense,the topological transitivity of the system is proved;( 3) the system is topological mixing;( 4) by means of discussing the positive expansiveness,the result that the system is chaos in the sense of Devaney is obtained.更多还原