标题： Rd-作用的定向扩张性以及彭罗斯密铺 显示英文标题

标题： Directional Expansiveness for Rd-Actions and for Penrose Tilings

摘要： 我们定义并研究了在紧致度量空间 X 上的\mathbb{R}^d 作用 T 的两种方向扩张性，弱和强。 我们证明对于\mathbb{R}^2 有限局部复杂性（FLC）的铺砌动力系统，弱扩张性和强扩张性是相同的，并且都等价于一个简单的编码性质。 然后我们证明对于 Penrose 铺砌动力系统，它具有 FLC，恰好有五个非扩张方向，这些方向垂直于五次单位根。 我们还研究了 Raphael Robinson 的 24 张 Penrose Wang 瓷砖，并证明相应的 Penrose Wang 瓷砖动力系统是严格遍历的。 最后，我们研究了 Penrose Wang 瓷砖系统的两种变形，一种是将所有正方形 Wang 瓷砖变形为 2\pi /5 菱形，另一种是将其变形为一组十一张四边形瓷砖。 我们证明这两种变形都与 Penrose 铺砌动力系统拓扑共轭。 显示英文摘要

摘要： We define and study two kinds of directional expansiveness, weak and strong, for an action T of \mathbb{R}^d on a compact metric space X. We show that for \mathbb{R}^2 finite local complexity (FLC) tiling dynamical systems, weak and strong expansiveness are the same, and are both equivalent to a simple coding property. Then we show for the Penrose tiling dynamical system, which is FLC, there are exactly five non expansive directions, the directions perpendicular to the 5th roots of unity. We also study Raphael Robinson's set of 24 Penrose Wang tiles and show the corresponding Penrose Wang tile dynamical system is strictly ergodic. Finally, we study two deformations of the Penrose Wang tile system, one where the square Wang tiles are all deformed into a 2\pi/5 rhombus, and another where they are deformed into a set of eleven tetragon tiles. We show both of these are topologically conjugate to the Penrose tiling dynamical system.