Spectral problem on quasi-periodic structure

我们利用Jeong-yup Lee开发了一个实用的算法来检验具有Pisot族条件的自仿射平移动力学闭合轨道的纯离散性。Pisot数通常表现为自诱导结构的膨胀常数。在与R.Okazaki，J.Luo，J.THuswaldner和W.Steiner的联合论文中，我们在平面形状的自相似解剖问题中观察到了类似的Pisot膨胀。利用Benoit Loridant，我们成功地给出了自仿射镶嵌边界的一种标准参数化，并展示了它在其拓扑分类中的有效性。

With Jeong-Yup Lee we developed a practical algorithm to check pure discreteness of translation dynamics of the orbit closure of self-affine tilings with Pisot family condition. Pisot numbers often appears as dilation constants of self-inducing structures. We observed similar Pisot dilations in the self-similar dissection problem of planar shapes in the joint paper with R. Okazaki, J. Luo, J. Thuswaldner and W. Steiner. With Benoit Loridant, we succeeded in giving a standard parameterization of boundaries of self-affine tilings and showed its effectiveness in their topological classification.