论文标题
替代斜利与先验通货膨胀因子
Substitution tilings with transcendental inflation factor
论文作者
论文摘要
对于任何$λ> 2 $，我们在无限字母上构建一个替代，这会产生带有通货膨胀因子$λ$的替换瓷砖。特别是，我们获得了具有先验通货膨胀因子的替代系统的第一类示例，这些因素具有有限字母上的原始替代品所享有的常规动力学特性。我们表明，相关的子迁移和平铺动力学系统都是严格的，这与基础替代操作员的准紧密性有关。我们还提供具有先验通货膨胀因子$λ$的明确替代。
For any $λ>2$, we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor $λ$. In particular, we obtain the first class of examples of substitutive systems with transcendental inflation factors that possess usual dynamical properties enjoyed by primitive substitutions on finite alphabets. We show that both the associated subshift and tiling dynamical systems are strictly ergodic, which is related to the quasicompactness of the underlying substitution operator. We also provide an explicit substitution with transcendental inflation factor $λ$.
