一个自相似集的分形维数与测度的计算  

Calculation of Fractal Dimension and Measure of a Self Similar Set

作　　者：周涛涛 

机构地区：[1]东华理工大学理学院,江西 南昌

出　　处：《理论数学》2023年第12期3559-3564,共6页Pure Mathematics

摘　　要：有一些分形集是由部分与整体以某种方式相似形成的,比如说Cantor三分集。Falconer提出了自相似集的概念,并且研究了计算其维数的方法。本文将这一方法应用到构造的一个自相似集F中,求出集合F的分形维数,并且用定义求出集合F的Hausdorff测度。There are some fractal sets that are formed by parts that are similar to the whole in some way, such as the Cantor triadic set. Falconer proposed the concept of self-similar sets and studied the method of calculating its dimensions. This paper applies this method to a constructed self-similar set F, finds the fractal dimension of the set F, and uses the definition to find the Hausdorff measure of the set F.

关 键 词：自相似集 HAUSDORFF测度 分形维数 

分 类 号：O17[理学—数学]