Self-similar Sets as Hyperbolic Boundaries
Self-similar Sets as Hyperbolic Boundaries
复制标题
DOI：
10.1512/iumj.2009.58.3639
复制
发表时间：
2009
影响因子：
1.1
通讯作者：
K. Lau;Xiang-Yang Wang
中科院分区：
文献类型：
--
作者：
K. Lau;Xiang-Yang Wang
我们证明了对于满足开集条件的相似的迭代函数系统{S j} N j=1，在表示符号空间中存在使其成为双曲图的自然图结构，并且双曲边界同胚于{S j} N j=1生成的自相似集。
We show that, for an iterated function system {S j } N j= 1 of similitudes that satisfies the open set condition, there is a natural graph structure in the representing symbolic space to make it a hyperbolic graph, and the hyperbolic boundary is homeomorphic to the self-similar set generated by {S j } N j=1 .