几乎可加势商的“发散集”的重分形分析

Multifractal analysis on the divergent set for the ratio of almost additive potentials

研究一类非一致扩张系统中几乎可加势商的"发散集"的Hausdorff维数谱的重分形分析.利用拼接n-级Bernoulli测度和构造Moran集的方法,证明在该系统中几乎可加势商的"发散集"的Hausdorff维数具有"择一性".

We discussed the multifractal analysis on the divergent set for the ratio of almost additive potentials in a class of one dimensional non-uniformly expanding systems and proved that the divergent set carried full Hausdorff dimension unless it is empty.