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《Journal of Chongqing Normal University(Natural Science)》 2018-04
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The Research of Dynamical Properties of the Product Space

ZHOU Shuang;JIN Yuguang;College of Mathematics Science,Chongqing Normal University;  
[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 f_1×f_2 is topological stability if only and if f_1 and f_2 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.
【Fund】: 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)
【CateGory Index】: O189.1
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