单峰映射允许搓揉序列的Hausdorff维数和测度

单峰映射允许搓揉序列的Hausdorff维数和测度

张爱华, 廖公夫

吉林大学数学研究所，长春 130012

收稿日期:2004-10-20 修回日期:1900-01-01 出版日期:2005-01-26 发布日期:2005-01-20
通讯作者: 廖公夫

Hausdorff Dimension and Measure of Admissible Kneading Sequences to Unimodal Mapping

ZHANG Ai-hua, LIAO Gong-fu

Institute of Mathematics, Jilin University, Changchun 130012, China

Received:2004-10-20 Revised:1900-01-01 Online:2005-01-26 Published:2005-01-20
Contact: LIAO Gong-fu

摘要/Abstract

摘要： 利用Hausdorff维数和Hausdorff测度, 对单峰映射的允许搓揉序列的集合给出定量刻画, 证明了该集合在两个符号的单边符号空间中Hausdorff维数是1, 1维Hausdorff测度是0.这与传统的定性分析相比, 结果更有意义.

关键词: 单峰映射, 搓揉序列, Hausdorff维数, Hausdorff测度

Abstract: Using the tools of Hausdorff dimension and Hausdorff measure, we give quantitative version for the set of admissible kneading sequences to unimodal mappings. It is proved for the set that the Hausdorff dimension is 1 and the 1-dimension Hausdorff measure is zero in one-sided symbolic space with two symbols， which are more profound than those obtained by traditional qualitative analysis.

Key words: unimodal mapping, kneading sequence, Hausdorff dimension, Hausdorff measure

中图分类号:

O189.1

张爱华, 廖公夫. 单峰映射允许搓揉序列的Hausdorff维数和测度[J]. J4, 2005, 43(01): 45-46.

ZHANG Ai-hua, LIAO Gong-fu. Hausdorff Dimension and Measure of Admissible Kneading Sequences to Unimodal Mapping[J]. J4, 2005, 43(01): 45-46.

[1]	廖公夫, 楚振燕, 范钦杰. 一类区间映射非游荡集的Hausdorff维数[J]. J4, 2009, 47(4): 749-751.
[2]	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.
[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.