几乎可加势的“历史点集”的Hausdorff维数  

Hausdorff dimension of historic set for almost additive potentials

作　　者：马冠忠[1] 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)

机构地区：[1]安阳师范学院数学与统计学院,河南安阳455000 [2]安阳师范学院图书馆采编部,河南安阳455000

出　　处：《高校应用数学学报（A辑）》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)

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.

关 键 词：几乎可加势 MORAN集 "历史点集" 非一致扩张 

分 类 号：O192[理学—数学]