gcf的度量性质对于参数函数的相依性

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1、吉首大学硕士学位论文GCF的度量性质对于参数函数的相依性吴茜二〇一八年五月分类号密级公开UDC单位代码吉首大学硕士学位论文GCF的度量性质对于参数函数的相依性Thedependenceofmetricpropertiesofgeneralizedcontinuedfractiononparameterfunction研究生姓名吴茜指导教师钟婷教授学科专业数学研究方向分形几何与连分数动力系统提交论文日期年月日论文答辩日期年月日答辩委员会主席论文评阅人二〇一八年五月目录目录摘要························

2、·······································································iABSTRACT·······················································································ii第1章绪论·······················································································11

3、.1问题的研究背景.............................................................................................11.2问题的研究现状.............................................................................................11.3本文的结构安排..............................................

4、...............................................2第2章预备知识···············································································32.1一般连分数的定义及基本性质.....................................................................32.2实数的正规连分数展式.............................

5、....................................................42.3GCF展式的定义及基本运算性质................................................................62.4Hausdorff维数..............................................................................................11第3章本文的主要结果及证明····

6、·······················································133.1GCF展式的部分现有结果..........................................................................133.2RCF集R()B及GCF集GB()......................................................................143.3参量wk()k1时GB()与R()B

7、的维数关系............................................1513.4wk()ckk时，GB()与R()B的维数关系....................................19第4章推论与总结··········································································224.1关于GB()的Hausdorff维数的进一步讨论.............................

8、..................224.2关于渐近分式的一点讨论...........................................................................244.3GCF展式研究有待解决的主要问题.............................