乘积空间动力性质的研究  

The Research of Dynamical Properties of the Product Space

作　　者：周双 金渝光 ZHOU Shuang;JIN Yuguang(College of Mathematics Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2018年第4期70-73,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11471061);2013年重庆高校创新团队建设计划(No.KJPB201308);重庆师范大学博士科研项目(No.17XLB001);重庆师范大学国家基金预研项目(No.16XYY21)

摘　　要：【目的】研究(X×Y,f×g)和(X,f)及(Y,g)之间动力性质的关系。【方法】将个体空间的动力性质推广到乘积空间。【结果】1)EP(f×g)=EP(f)×EP(g),其中EP(f)表示f的所有终于周期点的集合,EP(g)表示g的所有终于周期点的集合;2)f×g为可扩的充分必要条件是f与g分别为可扩的;3)若环面连续自映射可以分解成两个圆周连续自映射,则f_1×f_2具有拓扑稳定性的充分必要条件是f_1与f_2分别具有拓扑稳定性;4)若f×g为极小的,则f与g分别为极小的。【结论】乘积空间与个体空间在终于周期点集、拓扑可扩上是等价的,其中在一定特殊条件下拓扑稳定性是等价的,但在拓扑极小和拓扑传递的性质上却是不等价的。[Purposes]It mainly studies the relations of dynamical properties of（X×Y,f×g）,（X,f）,and（Y,g）.[Methods]The dynamic properties of the individual space are extended to the product space.[Findings]1）EP（f×g）=EP（f）×EP（g）,where EP（f）and EP（g）are eventually periodic points sets of fand g,respectively;2）f×gis topological expansive if only and if f and gare topological expansive,respectively;3）If a continuous self-mapping of torus can be decomposed into two consecutive circular self-mapping,then f1×f2 is topological stability if only and if f1 and f2 are topological stability respectively;4）If f×gis minimal,then fand gare minimal,respectively.[Conclusions]The topological expansive of the product space is the same as that of the individual space in the eventually periodic points set,where the topological stability is equivalent under certain special conditions,but the minimality and topological transitivity are is not equivalent between the product space and the individual space.

关 键 词：终于周期点 拓扑可扩 拓扑稳定性 

分 类 号：O189.1[理学—数学]