Devaney混沌的等价刻画

Equivalent charactertions of Devaney chaos

本文将Devaney混沌定义从度量空间推广到一般拓扑空间.在一般拓扑空间中分别得到了Devaney混沌的两组等价刻画.作为这两组等价刻画的推论:如果实数区间I或紧度量空间X上的连续自映射f对于任意两个非空开子集都共享同一周期轨,则f是Li-Yorke混沌映射.最后的两个例子部分地说明本文所得结果在应用中的有效性.

The definition of Devaney chaos is generalized characterizations of Devaney chaos on a topology space obtained： a continuous self mapping f：X→ X is chaotic from a metric space to a topology space. Two groups of equivalent are proved. As the corollary of the above results, the following is in the sense of Li-Yorke if any two non-empty open subsets share a periodic orbit off, where X is an interval or a compact metric space. Finally, two examples are revealed to illustrate the validity in the applications of the above results.