| 关于连续映射半群拓扑熵的一点注记 |
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| 引用本文： | 田延国,马东魁. 关于连续映射半群拓扑熵的一点注记[J]. 数学杂志, 2017, 37(4): 792-796 |
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| 作者姓名： | 田延国 马东魁 |
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| 作者单位： | 华南理工大学数学学院, 广东 广州 510641,华南理工大学数学学院, 广东 广州 510641 |
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| 基金项目： | 国家自然科学基金资助（11671149）；广东省自然科学基金资助（2014A030313230）；中央高校基础研究基金资助（SCUT（2015ZZ055；2015ZZ127））. |
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| 摘 要： | 本文研究了度量空间中连续映射构成半群的拓扑熵.利用Patr′ao~([8])的方法,给出了度量空间中两种有限个连续映射构成的半群的拓扑d-熵的定义,比较了两种拓扑d-熵的大小.证明了局部紧致可分度量空间上有限个真映射构成的半群的拓扑d-熵和它的一点紧化空间上对应的拓扑熵相等.上面结果推广了Patr′ao的相应结论.
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| 关 键 词： | 拓扑熵 半群 真映射 度量空间 |
| 收稿时间： | 2016-08-03 |
| 修稿时间： | 2016-10-31 |
A REMARK ON THE TOPOLOGICAL ENTROPY OF A SEMIGROUP OF CONTINUOUS MAPS |
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| TIAN Yan-guo and MA Dong-kui. A REMARK ON THE TOPOLOGICAL ENTROPY OF A SEMIGROUP OF CONTINUOUS MAPS[J]. Journal of Mathematics, 2017, 37(4): 792-796 |
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| Authors: | TIAN Yan-guo and MA Dong-kui |
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| Affiliation: | School of Mathematics, South China University of Technology, Guangzhou, 510641, China and School of Mathematics, South China University of Technology, Guangzhou, 510641, China |
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| Abstract: | In this paper, we study the topological entropy of a semigroup of continuous maps on a metric space. By using Patráo[8] method, we give two deflnitions of topological d -entropy of a semigroup generated by flnite continuous maps on a metric space, the size of these two d-entropies are compared. We also show that the topological d-entropy of the semigroup generated by flnite proper maps on a locally compact separable metric space and the topological entropy on its one-point compactiflcation space coincide, which extend the results obtained by Patráo. |
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| Keywords: | topological entropy semigroup proper maps metric space |
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