[1]吴华明.n方体连续自映射混沌集合的Hausdorff维数[J].四川师范大学学报(自然科学版),2019,(05):633-638.[doi:10.3969/j.issn.1001-8395.2019.05.010]
 WU Huaming.Hausdorff Dimension of Chaotic Sets Caused by a Continuous Self-map on In[J].Journal of SichuanNormal University,2019,(05):633-638.[doi:10.3969/j.issn.1001-8395.2019.05.010]
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n方体连续自映射混沌集合的Hausdorff维数()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年05期
页码:
633-638
栏目:
基础理论
出版日期:
2019-07-15

文章信息/Info

Title:
Hausdorff Dimension of Chaotic Sets Caused by a Continuous Self-map on In
文章编号:
1001-8395(2019)05-0633-06
作者:
吴华明
岭南师范学院 数学与统计学院, 广东 湛江 524048
Author(s):
WU Huaming
School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, Guangdong
关键词:
混沌集合 Hausdorff维数 In上连续自映射 高维笛卡尔积
Keywords:
chaotic sets Hausdorff dimension continuous self-map on igh dimensional Cartesian product
分类号:
O192
DOI:
10.3969/j.issn.1001-8395.2019.05.010
文献标志码:
A
摘要:
把线段、方体自映射混沌集合的Hausdorff维数的有关结果推广到n方体上,证明在C0(In)中存在一个剩余集R,使对每一f∈R,如果集合CIn对f是Li-Yorke混沌的,则dimH(C)≤n-1.对于高维笛卡尔积的情形,也得到类似的结果,即在C0(Ini,Ini)中存在一个剩余集Ri
Abstract:
This paper extends the results of Hausdorff dimension of chaotic sets caused by continuous self-maps on I and I2 to n-dimensional cube.We prove that there is a residual set R in C0(In), if set CIn is chaotic for any given f∈R in the sense of Li-Yorke, then dimH(C)≤n-1.Similarly way, the results on high dimensional Cartesian product can be obtained.That is, there is residual sets Ri in C0(Ini,Ini) such that for any fi∈Ri,i=1,2, if set CiIni is chaotic in the sense of Li-Yorke, then dimH(C1×C2)≤n-1.chaotic sets; Hausdorff dimension; continuous self-map on In.

参考文献/References:

[1] IVAN M.Continuous chaotic functions of an interval have generically small scrambled sets[J].Bull Austral Math Soc,1988,37(1):89-92.
[2] LI T Y, YORKE J.Period 3 implies chaos[J].Am Math Monthly,1975,82(10):985-992.
[3] 顾荣宝.线段自映射浑沌集合的Hausdorff维数[J].科学通报,1996,41(18):1633-1635.
[4] 吴华明.I2连续自映射混沌集合的Hausdorff维数[J].华南师范大学学报(自然科学版),2002,34(2):45-51.
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备注/Memo

备注/Memo:
收稿日期:2018-01-02 接受日期:2018-03-16
基金项目:国家自然科学基金(11561019)
作者简介:吴华明(1961—),男,教授,主要从事符号动力系统、数论的研究,E-mail:wuhuam3329@126.com
更新日期/Last Update: 2019-07-15