摘要
本文研究了拓扑群作用下乘积空间中G-极小性、G-混合性和G-链回归点的动力学问题.利用乘积映射与分映射之间的方法,获得如下结果:(1)乘积映射f×g是G-极小映射当且仅当f是G_1-极小映射,g是G_2-极小映射;(2)乘积映射f×g是G-混合映射当且仅当f是G_1-混合映射,g是G_2-混合映射;(3) CR_G(f×g)=CR_(G_1)(f)×CR_(G_2)(g).从而推广了乘积空间中极小性、混合性和链回归点的结果.
In this paper,the dynamical problem of G-minimality property,G-mixing property and G-chain recurrent point are investigated in the product space under the action of topological group.By using the method between product mapping and sub mapping,the following results are obtained.(1)The product map f×g is a G-minimality map if and only if the map f is a G1-minimality map and the map g is a G2-minimality map;(2)The product map f×g is a G-mixing map if and only if the map f is a G1-mixing map and the map g is a G2-mixing map;(3)CRG(f×g)=CRG1(f)×CRG2(g),which generalize the results of minimality property,mixing property and chain recurrent point in the product space.
作者
冀占江
张更容
JI Zhan-jiang;ZHANG Geng-rong(School of Data Science and Software Engineering,Wuzhou University,Wuzhou 543002,China;Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System,Wuzhou University,Wuzhou 543002,China;Mathematics and Computational Science,Hunnan First Normal University,Changsha 410205,China)
出处
《数学杂志》
2019年第3期399-404,共6页
Journal of Mathematics
基金
国家自然科学基金资助(11461002)
湖南自然科学基金资助(2018JJ2074)
广西自然科学基金资助(2016GXNSFAA380317)
广西高校中青年教师科研基础能力提升项目(2019KY0681)
梧州学院校级科研项目资助(2017C001)
