满足弱分离条件的齐次Moran-like集

齐次Moran集是自相似集的推广,具有在逐阶构造中基本元的相互位置及压缩比可以改变的特点。首先,定义了齐次Moran-like集,也就是用弱分离条件代替了齐次Moran集中的开集条件;然后,讨论了齐次Moran-like集的有关性质,得到了对于Moran-like集的更加精细化的计盒原理。

Homogeneous Moran-like Set with Weak Separation Condition

The homogeneous Moran set is a generalization of self-similar sets.The placements of the basic sets at each step of the constructions can be arbitrary,and the contraction ratios may be different at each step.In this paper,the homogeneous Moran-like set was defined,i.e.,using the weak separation condition instead of the open set condition of the homogeneous Moran set.Then the relevant properties of the homogeneous Moran-like set is discussed and the refinement version of the standard box-counting principle for the Moran-like set is proved.