| 拓扑遍历与拓扑双重遍历 |
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| 引用本文： | 杨润生.拓扑遍历与拓扑双重遍历[J].数学学报,2003,46(3):555-560. |
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| 作者姓名： | 杨润生 |
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| 作者单位： | 南京师范大学数学与计算机科学学院,南京,210097 |
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| 基金项目： | 国家自然科学基金资助项目(10271057)，江苏省自然科学基金资助项目(BK2001108) |
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| 摘 要： | 令X为紧致度量空间,f:X→X为连续映射,U,V为X的任意非空开集,若{n>0|fn(U)∩V≠ )为正上密度集,则称f拓扑遍历.f拓扑双重遍历意味着f×f拓扑遍历.本文在2]的基础上进一步讨论拓扑遍历与拓扑双重遍历映射的性质.
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| 关 键 词： | 拓扑遍历 拓扑双重遍历 等度连续 处处混沌 |
| 文章编号： | 0583-1431(2003)03-0555-06 |
| 修稿时间： | 2001年3月14日 |
Topological Ergodicity and Topological Double Ergodicity |
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| Run Sheng YANG.Topological Ergodicity and Topological Double Ergodicity[J].Acta Mathematica Sinica,2003,46(3):555-560. |
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| Authors: | Run Sheng YANG |
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| Institution: | Run Sheng YANG
(College of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P. R. China) |
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| Abstract: | Let X be a compact metric space and f : X →X a continuous onto map. f is called topologically ergodic if for any nonempty open sets U, V of X, {n > O | fn(U)∪ V ≠} is a set of positive upper density. Topological double ergodicity means that f@f is topologically ergodic. In this paper, we shall use the results in 2] to study the properties of topologically ergodic maps and topologically double ergodic maps. |
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| Keywords: | Topologically ergodic Topologically double ergodic Equicontinuous Everywhere chaos |
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