论文标题
关于非周期性自我易于瓷砖的算术进行的
On arithmetic progressions in non-periodic self-affine tilings
论文作者
论文摘要
我们研究了r^d中贴片的重复。特别是，我们研究了算术进程的存在和不存在。我们首先表明，自我处理瓷砖的扩展图的算术条件意味着某些一维算术进程的不存在。接下来，我们表明，对于某些类别的自我效果瓷砖，全级无限算术渐进，纯离散的动力学频谱和限制周期性的存在都是等效的。我们结束了完整的图片，以完整地描绘了R^d中的自相似瓷砖中全级无限算术进程的存在/不存在。
We study the repetition of patches in self-affine tilings in R^d. In particular, we study the existence and non-existence of arithmetic progressions. We first show that an arithmetic condition of the expansion map for a self-affine tiling implies the non-existence of certain one-dimensional arithmetic progressions. Next, we show that the existence of full-rank infinite arithmetic progressions, pure discrete dynamical spectrum, and limit periodicity are all equivalent for a certain class of self-affine tilings. We finish by giving a complete picture for the existence/non-existence of full-rank infinite arithmetic progressions in the self-similar tilings in R^d.
