论文标题
Lipschitz的贝德福德 - 麦克木糖地毯与均匀水平纤维的分类
Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers
论文作者
论文摘要
令$ {\ cal m} _ {t，v，r}（n，m）$，$ 2 \ 2 \ leq m <n $，是自动式地毯的收集，它们具有扩展的矩阵$ \ diag（n，m）$，这些矩阵（n，m）$完全断开，具有空置的行，具有统一的空缺且具有统一的水平纤维。在本文中，我们介绍了公制空间的结构树的概念，因此，由于这个新概念，我们完全表征了$ {\ cal m} _ {t，v，v，r}（n，m）$的两个地毯是lipschitz等效的。
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.
