具有相同不变集的迭代函数系统的关系  

Relationship of two Iterated Function System Which Have the Same Invariant Set

作　　者：鲁杏杰[1] 张瑞[1] 张润莲[1] 

机构地区：[1]华中师范大学数学与统计学院,湖北武汉430079

出　　处：《四川理工学院学报（自然科学版）》2007年第6期19-22,共4页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：两个迭代函数系统,其中一个迭代函数系统中的压缩映射可以由另一个系统中的压缩映射函数迭代而得,通过用多重指标I来代表迭代关系,在建立的坐标映射π是1—1的情况下,有生成相同不变集和I安全等价;并且在不变集上加上测度结构后,生成相同不变测度和I胎紧等价。There are two iterated function systems, one＇s contraction mappings can be obtained by iterating the contraction mappings of the other. If we use multi-index to represent the relation of the two systems, then in the condition that the establishment map π is one--one, we have： the generated invariant sets are the same if and only if I is secure; further more, if we impose measurable construction on the invariant set, then the generated invariant measures are the same if and only if I is tight.

关 键 词：不变测度 不变集 安全 胎紧 

分 类 号：O174.12[理学—数学]