摘要
研究了一类非一致扩张系统中几乎可加势的"历史点集"的Hausdorff维数问题.利用构造Moran集和拼接n-级Bernoulli测度的方法,证明了在该系统中几乎可加势的"历史点集"的Hausdorff维数具有"择一性",即若"历史点集"非空,则它具有满的Hausdorff维数.
The Hausdorff dimension of the"Historic set"for the almost additive potentials in a class of non-uniformly expanding systems is discussed.Using techniques of constructing"Moran set"and assembling n-level bernoulli measures,the paper proves that the Hausdorff dimension of the\Historic set"in this class of systems has"dichotomy",i.e.if the"Historic set"is not empty set,it will has full Hausdorff dimension.
作者
马冠忠
袁瑰霞
MA Guan-zhong;YUAN Gui-xia(School of Mathematics and Statistics,Anyang Normal University,Anyang 455000,China;Library Collection Department,Anyang Normal University,Anyang 455000,China)
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2018年第4期489-500,共12页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(11371055)
河南省高校重点科研项目(18A110007)
安阳师范学院科研培育基金(AYNUKP-2017-B21)
