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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Patráo[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Patráo的相应结论. |
| 关键词: 拓扑熵 半群 真映射 度量空间 |
| DOI： |
| 分类号:O189.1 |
| 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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| A REMARK ON THE TOPOLOGICAL ENTROPY OF A SEMIGROUP OF CONTINUOUS MAPS |
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TIAN Yan-guo,MA Dong-kui
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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. |
| Key words: topological entropy semigroup proper maps metric space |
