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| 连续自映射的拓扑r-熵及其性质 | |
| 引用本文： | 任蕴丽,卢占会,樊丽丽,吕金凤,何尚琴.连续自映射的拓扑r-熵及其性质[J].华北电力大学学报,2009,36(4). |
| 作者姓名： | 任蕴丽 卢占会 樊丽丽 吕金凤 何尚琴 |
| 作者单位： | 1. 河北科技师范学院数理系,河北秦皇岛,066004 2. 华北电力大学数理学院,河北保定,071003 3. 唐山师范学院数信系,河北唐山,063000 |
| 基金项目： | 河北省自然科学基金，唐山师范学院自然科学研究发展基金 |
| 摘 要： | 针对紧致度量空间上的连续自映射,本文给出了拓扑熵的一种新的定义,并讨论了这种拓扑熵的一些重要性质。证明了该拓扑熵与度量的选取无关,是拓扑共轭不变量,该拓扑熵对迭代系统具有可加性。同时,就系统在非游荡点集上的限制的这种拓扑熵与原系统的熵之间的关系进行了讨论,得到二者之间的一个不等式关系。 |
| 关 键 词： | 拓扑r-熵 拓扑熵 非游荡点集 拓扑共轭 |
Topological r-entropy of a continuous self-mapping and its properties |
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| REN Yun-li,LU Zhan-hui,FAN Li-li,LV Jin-feng,HE Shang-qin.Topological r-entropy of a continuous self-mapping and its properties[J].Journal of North China Electric Power University,2009,36(4). | |
| Authors: | REN Yun-li LU Zhan-hui FAN Li-li LV Jin-feng HE Shang-qin |
| Affiliation: | 1.Department of Mathematics and Physics;Hebei Normal University;Qinhuangdao 066004;China;2.School of Mathematics and Physics;North China Electric Power University;Baoding 071003;3.Department of Mathematics and Computer Science;Tangshan Teachers College;Tangshan 063000;China |
| Abstract: | This paper introduces a new concept of topological entropy of a continuous elfmapping on a compact metric space,and discusses some inportant properties of it.The following results are proved.The new topological entropy is independent of the choice of the metric and it is an invariant of topological conjugacy;the new topological entropy is addable for the iterations of the system.Meanwhile,the paper discusses the relationship between the new topological entropy of the retriction on the non-wandering set and ... |
| Keywords: | topological r-entropy topological entropy non-wandering set topological conjugacy |
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