ON THE DEGENERATE CENTER PROBLEM

被引：26
作者：
Gine, Jaume [1 ]
机构：
[1] Univ Lleida, Dept Matemat, Lleida 25001, Spain
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2011年 / 21卷 / 05期
关键词：
Degenerate center; first integral; Bautin method; essential variables; ANALYTIC INTEGRABILITY; DIFFERENTIAL-SYSTEMS; 2-DIMENSIONAL FLOWS; NILPOTENT CENTERS; SINGULAR POINTS; VECTOR-FIELDS; 1ST INTEGRALS; PLANE;
D O I：
10.1142/S0218127411029082
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, it is proved that any degenerate center is limit of a C(infinity) linear type center and when the degenerate center has an analytic first integral then it is limit of an analytic linear type center. A new method to detect integrability developed in [Gine & Santallusia, 2011] is applied to the degenerate center problem. Moreover, a review of the most important recent contributions to the degenerate center problem is given.
引用
收藏
页码：1383 / 1392
页数：10
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