Centennial history of Hilbert's 16th problem
Centennial history of Hilbert's 16th problem
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DOI：
10.1090/s0273-0979-02-00946-1
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发表时间：
2002-01-01
影响因子：
1.3
通讯作者：
Ilyashenko, Y
中科院分区：
文献类型：
--
作者：
Ilyashenko, Y
希尔伯特第十六题的第二部分处理平面上的多项式微分方程。即使是二次多项式，这个问题也没有解决。有几次试图解决这个问题都失败了。然而，这个问题在平面微分方程的几何理论，以及分岔理论、范式、叶分和代数几何中的一些主题方面取得了重大进展。下面将介绍这个问题的戏剧性历史以及相关的发展。
The second part of Hilbert's 16th problem deals with polynomial differential equations in the plane. It remains unsolved even for quadratic polynomials. There were several attempts to solve it that failed. Yet the problem inspired significant progress in the geometric theory of planar differential equations, as well as bifurcation theory, normal forms, foliations and some topics in algebraic geometry. The dramatic history of the problem, as well as related developments, are presented below.