盒维数概念的历史演变  

The Historical Evolution of the Concept of Box Dimension

作　　者：江南[1,2] JIANG Nan(Institute for Advanced Study in History of Science,Northwest University,Xi’an 710127;College of Science,Xi’an Shiyou University,Xi’an 710065,China)

机构地区：[1]西北大学科学史高等研究院,西安710127 [2]西安石油大学理学院,西安710065

出　　处：《自然辩证法研究》2020年第10期84-90,共7页Studies in Dialectics of Nature

基　　金：国家自然科学基金数学天元基金资助项目“分形简史”(11926503)。

摘　　要：盒维数是分形几何中一种应用非常广泛的分数维数,对它的研究最早可追溯至闵可夫斯基的工作。布利冈在闵可夫斯基容度理论的基础上建立了盒维数的最初模型,但没有给出具体的数学表达式。庞特里亚金和施尼勒尔曼紧随其后,定义了具有数学表达式的盒维数概念,不过尚缺乏严格性。柯尔莫戈洛夫和契霍洛夫借助容量和熵对盒维数概念进行了严格定义,推动了盒维数理论的发展。法尔科内集其大成,给出了现代意义下的盒维数概念,进一步完善了盒维数理论。Box dimension is a kind of fractional dimension which is widely used in fractal geometry. The study of box dimension can be traced back to Minkowski’s work on capacity theory. Bouligand built the initial model of box dimension on the basis of Minkowski’s theory, but gave no specific mathematical expression. Pontrjagin and Schnirelmann followed closely by defining the concept of box dimensions with mathematical expressions, but still lack of strictness. Kolmogorov and Tihomirov promoted the development of box dimension theory, and defined the concept of box dimension strictly through volume and entropy. Falconer made the great achievement by perfecting box dimension theory ulteriorly through defined the concept of box dimension in modern sense.

关 键 词：维数 分数维数 盒维数 分形几何 

分 类 号：N09[自然科学总论—科学技术哲学]