均匀水平纤维Bedford-McMullen地毯的Lipschitz分类
Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers
摘要：
设${\cal M}_{t,v,r}(n,m)$，$2\leq m<n$是具有扩张矩阵$\diag(n,m)$的自仿射地毯的集合，这些地毯是全不连通的，有空行，有均匀的水平纤维.本文引入了度量空间的结构树的概念，并利用这一新概念，完整地刻画了${\cal M}_{t,v,r}(n,m)$中两个地毯是Lipschitz等价的.
英文摘要：
Let ${\cal M}_{t,v,r}(n,m)$, $2\leq m<n$, be the collection of self-affine carpets with expanding matrix $\diag(n,m)$ which are totally disconnected, possessing vacant rows and with uniform horizontal fibers. In this paper, we introduce a notion of structure tree of a metric space, and thanks to this new notion, we completely characterize when two carpets in ${\cal M}_{t,v,r}(n,m)$ are Lipschitz equivalent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
