Analytic integrability for some degenerate planar vector fields

被引：20

作者：

Algaba, Antonio ^{[1
]}

Garcia, Cristobal ^{[1
]}

Gine, Jaume ^{[2
]}

机构：

[1] Univ Huelva, Ctr Invest Fis Teor & Matemat FIMAT, Dept Matemat, Huelva 21071, Spain

[2] Univ Lleida, Dept Matemat, Lleida 25001, Catalonia, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年 / 257卷 / 02期

关键词：

Nonlinear differential systems; Integrability problem; Degenerate center problem; DIFFERENTIAL-SYSTEMS; NILPOTENT CENTERS; REVERSIBILITY; FOCUS;

D O I：

10.1016/j.jde.2014.04.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the analytic integrability of degenerate vector fields of the form (y(3) + 2ax(3) y + ..., -x(5) - 3ax(2)y(2) + ...) around the origin. For these vector fields it is proved that integrability does not imply formal orbital equivalence to the Hamiltonian leading part. Moreover, it is shown the existence of a system in this class which has a center but is neither analytically integrable nor formal orbital reversible. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：549 / 565

页数：17

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