一些不變碎形的盒子和豪斯多夫維度

Abstract

在這篇論文中，考慮一些碎形不變集的盒子和豪斯多夫維度之間的關係。首先，我們將回顧一個著名的定理，此定理給出了充分的條件讓集合F的盒子和豪斯多夫維度是相等的，並提供一些這樣的例子當作一個例證。其次，我們考慮在整數乘法半群的作用下，符號序列空間的不變子集，此由[1]提出。這樣例子的盒子和豪斯多夫維度由不同做法說明它們是不同的。

In this thesis, the relationship between box and Hausdorff dimensions for a certain class of fractal invariant sets is considered. First, we shall review one well-known theorem that gives the sufficient conditions on a set F for which their box and Hausdorff dimensions are equal. Some examples are provided as an illustration. Second, we consider subsets of the symbolic sequence space that are invariant under the action of the semigroup of multiplicative integers, which are proposed in [1]. Box and Hausdorff dimensions of these examples are shown by different following their approach.