摘要
对应于定义在一个由有限字符集Ｓ＝｛ａｉ｜１≤ｉ≤ｔ｝ 所生成的自由半群Ｓ＊上的自同态映射θ，我们考虑Ｒｄ上的映射族（θ）＝｛Ｌ（ａｉ，ａｊ，ｋ，θ）｜１≤ｋ≤ｗ（ｉ，ｊ）｝ 及同态映射ｆ：Ｓ 满足在此框架上构造出广义递归集 ．此外当 为同态映射族时给出了其Ｈａｕｓｄｏｒｆｆ维数的上界估计；当 为共形压缩映射族时确定了其Ｈａｕｓｄｏｒｆｆ维数.
Associated with the endomorphism of the free semigroup S* generated by a finite alphabet S ={al, , at} there the collection of mappings on Rd and homomorphism f: S* Rd such that The generalized recurrent sets K [W] are constructed by means of those given above. Moreover the upper bound of the Hausdorff dimensions of K [W] are estimated when is the collection of homeomorphisms and the Hausdorff dimensions of K [W] are determined when is the collection of conformal contraction mappings.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1996年第1期125-132,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目
关键词
广义递归集
优配对
递归集
豪斯道夫维数
generalized recurrent set, Hausdorff dimension, resolvable condition, well matched
