论文标题
紧凑字母的替换
Substitutions on compact alphabets
论文作者
论文摘要
我们开发了一种系统的方法来对紧凑型Hausdorff字母进行连续替换。着重于对不可约性和原始性的含义，我们强调了其（广义）亚班的拓扑动力学的重要特征。然后，我们根据相应替代运算符的光谱特性从崇高理论中进行了问题。这需要将标准的Perronius理论扩展到Banach Lattices的设置。作为应用程序，我们确定可计算标准，以保证替代运算符的准紧密度。这允许为多个示例验证唯一的牙齿。例如，得出的是，具有孤立点的字母上的每个原始长度替换都是独特的，这是当没有孤立点时失败的结果。
We develop a systematic approach to continuous substitutions on compact Hausdorff alphabets. Focussing on implications of irreducibility and primitivity, we highlight important features of the topological dynamics of their (generalised) subshifts. We then reframe questions from ergodic theory in terms of spectral properties of a corresponding substitution operator. This requires an extension of standard Perron--Frobenius theory to the setting of Banach lattices. As an application, we identify computable criteria that guarantee quasi-compactness of the substitution operator. This allows unique ergodicity to be verified for several classes of examples. For instance, it follows that every primitive and constant length substitution on an alphabet with an isolated point is uniquely ergodic, a result which fails when there are no isolated points.
