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| 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G1-极小映射，g是G2-极小映射；（2）乘积映射f×g是G-混合映射当且仅当f是G1-混合映射，g是G2-混合映射；（3）CRG（f×g）=CRG1（f）×CRG2（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. |
| 关键词: G-极小性 G-混合性 G-链回归点 乘积G-空间 |
| DOI： |
| 分类号:O189.11 |
| 基金项目: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）. |
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| G-MINIMALITY, G-MIXING AND G-CHAIN RECURRENT POINT OF THE PRODUCT G-SPACE |
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JI Zhan-jiang,ZHANG Geng-rong
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| Abstract: |
| 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. |
| Key words: G-minimality G-mixing G-chain recurrent point product G-space |
