一类4阶Feigenbaum映射的拟极限集

一类4阶Feigenbaum映射的拟极限集

王立娟¹, 张爱华²

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

收稿日期:2002-12-11 修回日期:1900-01-01 出版日期:2003-10-26 发布日期:2003-10-26
通讯作者: 王立娟

Likely Limit Sets of a 4-Order Feigenbaum’s Map

WANG Li-juan¹, ZHANG Ai-hua²

1. 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:2002-12-11 Revised:1900-01-01 Online:2003-10-26 Published:2003-10-26
Contact: WANG Li-juan

摘要/Abstract

摘要： 讨论一类4阶Feigenbaum映射的拟极限集及其Hausdorff维数, 并证明对任意t∈(0,log_3^1/2+12), 总存在一类具有简单轨的4阶非单谷Feigenbaum映射，它有一个以t为Hausdorff维数的拟极限集.

关键词: Feigenbaum映射, 拟极限集, Hausdorff维数, 简单轨

Abstract: On the basis of considering the likely limit sets of a 4-order Feigenbaum's map and their Hausdorff dimension, we have proved that for any t∈(0,log_{3^1/2+1_{2), there always exits such a 4-order nonsingle-valley Feigenbaum’s map which has a likely limit set with Hausdorff d imension t.}}

Key words: Feigenbaum’s map, likely limit sets, Hausdorff dimension, simple periodic orbits

中图分类号:

O189.1

王立娟, 张爱华. 一类4阶Feigenbaum映射的拟极限集[J]. J4, 2003, 41(04): 436-439.

WANG Li-juan, ZHANG Ai-hua. Likely Limit Sets of a 4-Order Feigenbaum’s Map[J]. J4, 2003, 41(04): 436-439.

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