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
DOI: 10.12677/PM.2018.86093, PDF,    科研立项经费支持
作者: 彭桐辉, 王亚琳, 徐玲芳, 马冠忠：安阳师范学院数学与统计学院，河南 安阳
关键词: 非一致扩张系统；渐近可加势；历史集；Non-Uniformly Expanding； Asymptotically Additive Potentials； Historic Set
摘要: 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”。
Abstract: 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.
文章引用：彭桐辉, 王亚琳, 徐玲芳, 马冠忠. 渐近可加势的“历史集”的Hausdorff维数谱[J]. 理论数学, 2018, 8(6): 688-698. https://doi.org/10.12677/PM.2018.86093

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