具有进位吸引子的区间映射  

Maps of the Interval with Adic Attractor

作　　者：廖公夫[1] 刘恒[1] 王立冬[2] 

机构地区：[1]吉林大学数学研究所,长春130012 [2]大连民族学院理学院,辽宁大连116600

出　　处：《数学年刊（A辑）》2006年第5期587-594,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19971035);吉林大学创新基金(No.2004CX051)资助的项目

摘　　要：对于一个具有n-进位吸引子的区间连续映射,证明了：“n不是2的方幂”是该映射具有正拓扑熵的充分条件但不是必要条件；探讨了函数方程f^3(λx)=λf(x)的一类解,并证明这类解中的每一个成员都有3-进位吸引子．The notion of adic attractor is introduced. For a continuous interval map with nadic attractor, the paper proves that the condition that n is not a power of 2 is sufficient but not necessary for the map to have positive topological entropy. And a class of solutions of the functional equation f^3（λx） = λf（x）, which will be proved to have 3-adic attractor, are investigated.

关 键 词：区间映射 进位吸引子 拓扑熵 

分 类 号：O189.33[理学—数学]