Centennial history of Hilbert's 16th problem

被引：327
作者：
Ilyashenko, Y
机构：
[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA
[2] Univ New Mexico, Albuquerque, NM 87131 USA
[3] Univ Colorado, Boulder, CO 80309 USA
来源：
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2002年 / 39卷 / 03期
关键词：
limit cycles; polynomial vector fields; normal forms; bifurcations; foliations; Abelian integrals;
D O I：
10.1090/S0273-0979-02-00946-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：301 / 354
页数：54
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