n方体连续自映射混沌集合的Hausdorff维数  

Hausdorff Dimension of Chaotic Sets Caused by a Continuous Self-map on I^n

作　　者：吴华明 WU Huaming(School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang 524048,Guangdong)

机构地区：[1]岭南师范学院数学与统计学院

出　　处：《四川师范大学学报（自然科学版）》2019年第5期633-638,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11561019)

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(I^n)中存在一个剩余集R,使对每一f∈R,如果集合C■I^n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C^0(I^ni,I^ni)中存在一个剩余集Ri,使得对于每个fi∈Ri,i=1,2,若集合Ci■I^ni对于fi而言是Li-Yorke混沌的,则dimH(C1×C2)≤n-1.This paper extends the results of Hausdorff dimension of chaotic sets caused by continuous self-maps on I and I^2 to n-dimensional cube.We prove that there is a residual set R in C^0(I^n),if set C■I^n 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 C^0(I^ni,I^n i)such that for any fi∈Ri,i=1,2,if set Ci■I^ni is chaotic in the sense of Li-Yorke,then dimH(C1×C2)≤n-1.

关 键 词：混沌集合 HAUSDORFF维数 I^n上连续自映射 高维笛卡尔积 

分 类 号：O192[理学—数学]