渐近可加势的“历史集”的Hausdorff维数谱

Spectrum of Hausdorff Dimension on the Historic Set of the Asymptotically Additive Potentials

研究了一类非一致扩张系统中渐进可加势的“历史集”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,证明了在该系统中渐近可加势的“历史集”的Hausdorff维数具有“择一性”。

Authors conduct multifractal analysis of historic set of the asymptotically additive potentials on a class of non-uniformly expanding systems. They prove that either the historic set is empty or carries full Hausdorff dimension.