齐次自相似集的多重分形谱分析

Analysis of the Multifractal Spectra of Uniformly Contracting Self-Similar Set

给出了齐次自相似集满足分离性质的一个充分条件,对于直线上的一致压缩映射族,若齐次压缩比小于各个压缩映射平移量之间的最小距离,则相应齐次自相似集满足开集条件,从而它的各种多重分形谱都相等,于是得到了重分形谱的一个简便求法.

We give a sufficient condition for an uniformly contracting self-similar set to have the separation property. For uniform contractions of the real line, the multifractal spectra of the associated uniformly contracting self-similar set give the same value if the contracting ratio is smaller than the minimum distance among all the translations. According to this we get a simple solution to the spectra.