符号空间转移自映射的有限型浑沌集合的Hausdorff测定  

Hausdorff Measure of the Finitely Chaotic Set Caused by the Shift Transformation on the One-sided Symbolic Space

作　　者：宋万干 

出　　处：《淮北煤师院学报（自然科学版）》1998年第2期4-8,共5页Journal of Huaibei Teachers College(Natural Sciences Edition)

摘　　要：本文讨论了（单边）符号空间ΣN的转移自映射σ引起的有限型浑沌，得到了如下结果：设｛mi｝是一个严格递增的正整数序列，则存在一个相对于序列｛mi｝而言的有限型浑沌集合，其1-维Hausdorff测度为1，等于ΣN的1-维Hausdorff测度；且若，其中为x的ω-极限集，则F中包含一个Borel集B，其1-维Hausdoer测度为1，从而F的1-维Hausdorff测度为1．In thes paper,it is discussed that the finite chaos caused by the shift transformation on the onesided symbolic space ΣN. It is shown that if {mi} is a strictly increasing sequence of posihve integers,then there exists a subset finitely chaohc with respect to the sequence {mi},such that 1 dimensional Hausdoarmeasure of C is one,equals to 1- dimensional Hausdoff measure of ΣN. Ifwhere ed,ed the ω-lint set of x, then there is a Borel subset B containedin the F with 1- dimensional Hausdoormeasure of B is one, therefore 1- dimensional Hausdorffmeasure ofF is one.

关 键 词：符号空间 转移自映射 有限型浑沌 测度 浑沌集合 

分 类 号：O189.1[理学—数学]