代数图递归迭代函数系与开集条件（英文）  

The Algebraic Graph-directed Iterated Function System and the Open Set Condition

作　　者：杨亚敏[1] 

机构地区：[1]华中农业大学理学院,湖北武汉430070

出　　处：《应用数学》2014年第2期457-461,共5页Mathematica Applicata

基　　金：the National Natural Science Foundation of China(11101169);the Fundamental Research Funds for the Central University(2010QC012)

摘　　要：本文研究R上一类代数图递归迭代函数系的开集条件与代数参数β之间的关系.我们证明若图递归迭代函数系满足开集条件且递归图是几何型的,则βs必是一个代数整数,其中s为图递归迭代函数系不变集的最大的Hausdorff维数.In this paper,we study the relation between the open set condition of a class of algebraic graph-directed iterated function systems on R and the algebraic parameters β. We show that if the system satisfies the open set condition and the graph is geometric, then β must be an algebraic integer, where s is the maximal Hausdorff dimension of the invariant sets of the system.

关 键 词：迭代函数系 开集条件 代数整数 HAUSDORFF维数 

分 类 号：O186[理学—数学] O172[理学—基础数学]