%0 Journal Article
%T 指数函数族非回归参数的Hausdorff维数<br>Hausdorff Dimension of Non-Recurrent Parameters in the Exponential Family
%A 陈姣汝
%A 丁杰
%J Advances in Applied Mathematics
%P 4498-4505
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/aam.2024.1310430
%X 本文主要探讨指数函数族中一类特殊参数&#8212;&#8212;非回归参数的Hausdorff维数问题&#65292;这一研究是在邱维元关于指数函数族逃逸参数的Hausdorff维数为2的重要发现基础上进行的自然延伸与深化。本文旨在证明&#65292;在给定的一个固定区域内&#65292;指数函数族中非回归且非逃逸参数的集合具有的Hausdorff维数严格小于某个给定的正数。<br>This paper primarily delves into the Hausdorff dimension of a special class of parameters within the exponential family&#8212;the non-recurrent parameters. This investigation constitutes a natural extension and deepening of Qiu&#8217;s seminal finding that the Hausdorff dimension of escaping parameters of the exponential family is 2. The objective of this paper is to prove that, within a given fixed region, the Hausdorff dimension of the set of non-escaping non-recurrent parameters in the exponential function family is strictly less than a specified positive number.
%K 非回归参数&#65292
%K 振荡参数&#65292
%K 有界参数&#65292
%K 指数函数&#65292
%K Hausdorff维数<br>Non-Recurrent Parameters
%K Oscillating Parameters
%K Bounded Parameters
%K Exponential Function
%K Hausdorff Dimension
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=97778