论文摘要
本文主要研究二元生成的Schottky群的性质.Schottky群是一类重要的Mo|¨bius变换群,也是一类特殊的Klein群.关于二元生成的Schottky群的性质,本文将从两个方面对二元生成的Schottky群进行研究.一方面,通过三个参数t1,t2和ρ的取值范围将二元生成的Schottky群分成八类,然后给出第三类,第六类和第八类的J（?）rgensen数,接着推导出这三类的等价定理.另一方面,利用Nielsen逆变换的定义,可以得到不同类二元生成的Schottky群的关系,进一步研究第三类,第六类和第八类的双曲变换.本文由五章构成.第一章主要介绍了二元生成的Schottky群研究的背景、意义及进展情况,并简单介绍了本文的主要工作.第二章介绍一些相关的概念和性质,并为后面三章的证明做铺垫.第三章研究了t1,t2和ρ这三个参数在Nielsen逆变换的转换,并发现:当j = 1,2时, Nj-1与Nj对t1,t2和ρ的作用相同.第四章介绍三类二元生成的Schottky群的J（?）rgensen数,并给出其具体形式.第五章研究三类二元生成的Schottky群在Nielsen逆变换下的关系,进一步得到它的一些相关性质.
论文目录
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