关于齐次Moran集的packing维数结果

数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 873-878.

关于齐次Moran集的packing维数结果

胡晓梅^1,2

1. 华中师范大学数学与统计学学院武汉 430079;
2. 湖北科技学院湖北咸宁 437100

收稿日期:2015-12-09 修回日期:2016-09-09 出版日期:2016-10-26 发布日期:2016-10-26
作者简介:胡晓梅,E-mail:xiaomeihu@163.com
基金资助:
国家自然科学基金（11271148）资助

Packing Dimensional Results for Homogeneous Moran Sets

Hu Xiaomei^1,2

1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079;
2. School of Mathematics and Statistics, Hubei University of Science and Technology, Hubei Xianning 437100

Received:2015-12-09 Revised:2016-09-09 Online:2016-10-26 Published:2016-10-26
Supported by:
Supported by the NSFC(11271148)

摘要/Abstract

摘要：

该文构造了一类特殊的齐次Moran集，称为{m_k}-拟齐次Cantor集，并讨论了它们的packing维数.通过调整序列{m_k}_k≥1的值，构造性证明了齐次Moran集packing维数的介值定理.此外，还得到了齐次Moran集的packing维数取得最小值的一个充分条件.

关键词: 齐次Moran集, {m_k}-Moran集, {m_k}-拟齐次Cantor集, Packing维数

Abstract:

In this paper, we construct a class of special homogeneous Moran set, called {m_k}-quasi homogeneous Cantor set and discuss their packing dimensions. By adjusting the value of {m_k}_k≥1, we constructively prove the intermediate value theorem about packing dimensions of the homogeneous Moran sets. Moreover, we obtain a sufficient condition that the packing dimension of homogeneous Moran sets may get the minimum value.

Key words: Homogeneous Moran set, {m_k}-Moran set, {m_k}-Quasi homogeneous Cantor set, Packing dimension

中图分类号:

O174.12

胡晓梅. 关于齐次Moran集的packing维数结果[J]. 数学物理学报, 2016, 36(5): 873-878.

Hu Xiaomei. Packing Dimensional Results for Homogeneous Moran Sets[J]. Acta mathematica scientia,Series A, 2016, 36(5): 873-878.