不具有简单轨的4阶非单谷Feigenbaum映射的拟极限集

不具有简单轨的4阶非单谷Feigenbaum映射的拟极限集

王立娟¹, 张爱华^1,2

1. 吉林大学数学学院数学系, 长春 130012; 2. 南京邮电学院应用数理系，南京 210003

收稿日期:2004-02-19 修回日期:1900-01-01 出版日期:2004-10-26 发布日期:2004-10-26
通讯作者: 王立娟

Likely limit sets of 4-order nonsingle-valley Feigenbaum's maps without simple periodic orbits

WANG Li-juan¹, ZHANG Ai-hua^1,2

1. Department of Mathematics, College of Mathematics, Jilin University, Changchun 130012, China;2. Department of Applied Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

Received:2004-02-19 Revised:1900-01-01 Online:2004-10-26 Published:2004-10-26
Contact: WANG Li-juan

摘要/Abstract

摘要： 讨论一类不具有简单轨的4阶Feigenbaum映射拟极限集的存在条件及其Hausdorff维数. 不具有简单轨的4阶Feigenbaum映射必然产生混沌，从而使拟极限集的存在性问题复杂化. 利用分形几何中的方法证明了此类映射拟极限集的存在性，并相应的对其Hausdorff维数做出估计. 最后给一个具体例子，说明确实存在不具有简单轨的4阶Feigenbaum映射.

关键词: Feigenbaum映射, 拟极限集, Hausdorff维数

Abstract: 4-order nonsingle-valley Feigenbaum's maps without simple periodic orbits must bring chaos, chaos also bring the complication of the problem on the existence of likely limit sets. We testified the existence of the maps' likely limit sets using the method of fractal geometry and estimated their Hausdorff dimension. In the end, we gave an idiographic example to proof the existence of 4-order nonsingle-valley Feigenbaum's maps without simple periodic orbits.

Key words: Feigenbaum's map, likely limit set, Hausdorff dimension

中图分类号:

O189.1

王立娟, 张爱华. 不具有简单轨的4阶非单谷Feigenbaum映射的拟极限集[J]. J4, 2004, 42(04): 499-501.

WANG Li-juan, ZHANG Ai-hua. Likely limit sets of 4-order nonsingle-valley Feigenbaum's maps without simple periodic orbits[J]. J4, 2004, 42(04): 499-501.

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