| 4阶非单谷Feigenbaum映射的拟极限集的Hausdorff维数与测度 |
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| 引用本文： | 王立娟,张爱华.4阶非单谷Feigenbaum映射的拟极限集的Hausdorff维数与测度[J].南京邮电大学学报(自然科学版),2006,26(3):49-51,57. |
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| 作者姓名： | 王立娟 张爱华 |
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| 作者单位： | 1. 嘉兴学院,数学与信息科学学院,浙江,嘉兴,314001
2. 南京邮电大学,数理学院,江苏,南京,210003 |
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| 摘 要： | 4阶非单谷Feigenbaum映射限制在其非游荡集上分为两个不同的共轭类，即具有简单轨的和不具有简单轨的。针对这两类不同的映射，构造性地证明了对给定的足够小的正数S，分别存在一类4阶非单谷Feigenbaum映射，使其拟极限集的Hausdorff维数恰好是S。其中，不具有简单轨的这类映射必然产生混沌，对其拟极限集的Haudorff测度进行了计算。
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| 关 键 词： | Feigenbaum 映射 拟极限集 Hausdorff 维数 Hausdorff 测度 |
| 文章编号： | 1673-5439（2006）03-0049-03 |
| 收稿时间： | 2005-09-12 |
| 修稿时间： | 2005-09-122005-10-31 |
Hausdorff Dimension and Measure of Likely Limit Sets of 4-Order Nonsingle-Valley Feigenbaum's Maps |
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| WNAG Liojuan, ZHANG Ai-hua.Hausdorff Dimension and Measure of Likely Limit Sets of 4-Order Nonsingle-Valley Feigenbaum''''s Maps[J].Journal of Nanjing University of Posts and Telecommunications,2006,26(3):49-51,57. |
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| Authors: | WNAG Liojuan ZHANG Ai-hua |
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| Institution: | 1. College of Mathematics and Information Science, Jiaxing University, Jiaxing 314001, China; 2. College of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China |
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| Abstract: | There are two types of topological conjugacy on 4-order nonsingle-valley Feigengaum's mapping which limited their nonwandering sets,i.e.with simple periodic orbits and without simple perodic orbits.In this paper,we proved that for enough small positive number s there always exists one kind of 4-order non single-valley Feigengaum's mapping without simple periodic orbits,definitely chaos will appear.We also estimated its Hausdorff measure. |
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| Keywords: | Feigenbaum's map Likely limit Hausdorff dimension Hausdorff measure |
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