论文标题
Jeandel-Rao Wang Shift中的非专业方向
Nonexpansive directions in the Jeandel-Rao Wang shift
论文作者
论文摘要
我们表明，$ \ {0，φ+3，-3φ+2，-φ+\ frac {5} {2} {2} \} $是notxpansive方向的斜率集，用于在Jeandel-rao Wang Shift中最小的亚换档，其中$ \φ=（$+=（1+\ sqrt =（1+\ sqrt}）该集合是一个拓扑不变的，允许将Jeandel-rao Wang的转移与其他次换档区分开。此外，我们描述了单位间隔的非理性旋转方面，沿非专业方向的康威蠕虫的两种分辨率的组合结构。介绍以非周期性王砖的图片结束，与康威（Conway）在Penrose Tilings的背景下所说的Cartwheel瓷砖相对应。本文以关于章鱼王偏移中章鱼的描述和基本孔的描述的开放性问题结束。
We show that $\{0,φ+3,-3φ+2,-φ+\frac{5}{2}\}$ is the set of slopes of nonexpansive directions for a minimal subshift in the Jeandel-Rao Wang shift, where $φ=(1+\sqrt{5})/2$ is the golden mean. This set is a topological invariant allowing to distinguish the Jeandel-Rao Wang shift from other subshifts. Moreover, we describe the combinatorial structure of the two resolutions of the Conway worms along the nonexpansive directions in terms of irrational rotations of the unit interval. The introduction finishes with pictures of nonperiodic Wang tilings corresponding to what Conway called the cartwheel tiling in the context of Penrose tilings. The article concludes with open questions regarding the description of octopods and essential holes in the Jeandel-Rao Wang shift.
