p阶Feigenbaum映射的拟极限集及其Hausdorff维数

J4 ›› 2009, Vol. 47 ›› Issue (05): 933-934.

p阶Feigenbaum映射的拟极限集及其Hausdorff维数

廖公夫^1,2, 汪威²

1. 吉林师范大学数学学院, 吉林四平 136000|2. 吉林大学数学研究所, 长春 130012

收稿日期:2009-05-14 出版日期:2009-09-26 发布日期:2009-11-03
通讯作者: 廖公夫 E-mail:liaogf@mail.jlu.edu.cn.

Likely Limit Sets of p-Order Feigenbaum’s Maps andTheir Hausdorff Dimensions

LIAO Gongfu^1,2, WANG Wei²

1. College of Mathematics, Jilin Normal University, Siping 136000, Jilin Province, China;
2. Institute of Mathematics, Jilin University, Changchun 130012, China

Received:2009-05-14 Online:2009-09-26 Published:2009-11-03
Contact: LIAO Gongfu E-mail:liaogf@mail.jlu.edu.cn.

摘要/Abstract

摘要：

通过研究Feigenbaum映射分形极限集的存在条件, 证明了对任何t∈(0,1), 存在一个p阶Feigenbaum映射, 使得其拟极限集的Hausdorff维数是t, 并在广泛意义下推广了已有的相应结果.

关键词: p阶Feigenbaum映射, 拟极限集, Hausdorff维数

Abstract:

Investigating the existence of the fractal limit sets of p-order Feigenbaum’s maps, we have proved that for any t∈(0,1), there exists such a p-order Feigenbaum’s map that the Hausdorff dimension of the likely limit set is t, by which some known relative results are generalized in the widest sense.

Key words: p-order Feigenbaum’s map, likely limit set, Hausdorff dimension

中图分类号:

O199.1

廖公夫, 汪威. p阶Feigenbaum映射的拟极限集及其Hausdorff维数[J]. J4, 2009, 47(05): 933-934.

LIAO Gong-Fu, HONG Wei. Likely Limit Sets of p-Order Feigenbaum’s Maps andTheir Hausdorff Dimensions[J]. J4, 2009, 47(05): 933-934.

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