0~1有限序列的无穷*积

0~1有限序列的无穷*积

黄桂丰¹, 范钦杰²

1. 海军大连舰艇学院基础部, 辽宁省大连 116018； 2. 吉林师范大学数学学院, 吉林省四平 136000

收稿日期:2007-04-16 修回日期:1900-01-01 出版日期:2007-11-26 发布日期:2007-11-26
通讯作者: 范钦杰

Infinite * Product for Finite Sequence of 0~1

HUANG Gui feng¹, FAN Qin jie²

1. Department of Basics, Dalian Naval Academy, Dalian 116018, Liaoning Province, China; 2. College of Mathematics, Jilin Normal University, Siping 136000, Jilin Province, China

Received:2007-04-16 Revised:1900-01-01 Online:2007-11-26 Published:2007-11-26
Contact: FAN Qin jie

摘要/Abstract

摘要： 研究Feigenbaum映射的搓揉序列, 定义了0~1有限序列的*积概念, 并利用*积的性质证明了所得的无穷序列必是符号空间中移位映射的一致几乎周期点, 进而推出任何p阶Feigenbaum映射的搓揉序列都是移位映射的一致几乎周期点, 而非周期点.

关键词: Feigenbaum映射, 重正化算子, 符号动力系统, 几乎周期性

Abstract: We investigated the kneading sequence of Feigenbaum’s map, definited the notion about * productfor finite sequence of 0~1, and proved via the properties of * product that such infinite sequences must be uniformly almost periodic points of the shift map in the symbolic space. Furthermore, we deduced that the kneading sequence for every porder Feigenbaum’s map is a uniformly almost periodic point of the shift map but not a periodic one.

Key words: Feigenbaum’s map, renormalization operator, symbolic dynamical system, almost periodic properties

中图分类号:

O189

黄桂丰, 范钦杰. 0~1有限序列的无穷*积[J]. J4, 2007, 45(06): 912-914.

HUANG Gui feng, FAN Qin jie. Infinite * Product for Finite Sequence of 0~1[J]. J4, 2007, 45(06): 912-914.

[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.
[2]	范钦杰, 王宏仁, 杜弈秋. 0-1符号空间上的*积子移位[J]. J4, 2008, 46(06): 1021-1024.
[3]	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.
[4]	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.