Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics

IF 0.7 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Archive for History of Exact Sciences Pub Date : 2020-06-29 DOI:10.1007/s00407-020-00250-3
Vladimir Dragović, Irina Goryuchkina
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引用次数: 3

Abstract

In this paper, we study the genesis and evolution of geometric ideas and techniques in investigations of movable singularities of algebraic ordinary differential equations. This leads us to the work of Mihailo Petrović on algebraic differential equations (ODEs) and in particular the geometric ideas expressed in his polygon method from the final years of the nineteenth century, which have been left completely unnoticed by the experts. This concept, also developed independently and in a somewhat different direction by Henry Fine, generalizes the famous Newton–Puiseux polygonal method and applies to algebraic ODEs rather than algebraic equations. Although remarkable, the Petrović legacy has been practically neglected in the modern literature, although the situation is less severe in the case of results of Fine. Therefore, we study the development of the ideas of Petrović and Fine and their places in contemporary mathematics.

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Petrović和Fine的多边形、代数常微分方程和当代数学
本文研究了代数常微分方程可动奇点研究中几何思想和技术的起源和发展。这就引出了Mihailo Petrović在代数微分方程(ODEs)方面的工作,特别是他在19世纪最后几年的多边形方法中表达的几何思想,这些思想被专家们完全忽视了。这个概念也由Henry Fine独立发展,并朝着不同的方向发展,推广了著名的Newton–Puiseux多边形方法,并适用于代数常微分方程,而不是代数方程。尽管Petrović的遗产引人注目,但在现代文学中却几乎被忽视了,尽管Fine的结果情况并不那么严重。因此,我们研究了Petrović和Fine思想的发展及其在当代数学中的地位。
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来源期刊
Archive for History of Exact Sciences
Archive for History of Exact Sciences 管理科学-科学史与科学哲学
CiteScore
1.30
自引率
20.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.
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