Nilpotent centres via inverse integrating factors

被引：13

作者：

Algaba, Antonio ^{[1
]}

Garcia, Cristobal ^{[1
]}

Gine, Jaume ^{[2
]}

机构：

[1] Univ Huelva, Fac Ciencias, Dept Matemat, Huelva, Spain

[2] Univ Lleida, Escola Politecn Super, Dept Matemat, Ave Jaume 2,69, Lleida 25001, Catalonia, Spain

来源：

EUROPEAN JOURNAL OF APPLIED MATHEMATICS | 2016年 / 27卷 / 05期

关键词：

non-linear differential systems; integrability problem; nilpotent centre problem; LIMIT-CYCLES; DIFFERENTIAL-EQUATIONS; SYSTEMS; INTEGRABILITY; REVERSIBILITY; BIFURCATIONS; EXISTENCE; MONODROMY; POINT;

D O I：

10.1017/S0956792516000103

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are interested in the nilpotent centre problem of planar analytic monodromic vector fields. It is known that the formal integrability is not enough to characterize such centres. More general objects are considered as the formal inverse integrating factors. However, the existence of a formal inverse integrating factor is not sufficient to describe all the nilpotent centres. For the family studied in this paper, it is enough.

引用

页码：781 / 795

页数：15

共 24 条

[11]

Andreev A., 1953, AKAD NAUK SSSR PRIKL, V17, P333

[12] REVERSIBILITY AND CLASSIFICATION OF NILPOTENT CENTERS [J].

BERTHIER, M ;

MOUSSU, R .

ANNALES DE L INSTITUT FOURIER, 1994, 44 (02) :465-494

[13]

Garcia I. A., 2016, J BIFUR CHAOS APPL S, V26

[14]

Garcia I. A., 2015, ANAL NILPOTENT CTR L

[15] Center problem for several differential equations via Cherkas' method [J].

Gasull, A ;

Torregrosa, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 228 (02) :322-343

[16] The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems [J].

Giacomini, Hector ;

Gine, Jaume ;

Llibre, Jaume .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 227 (02) :406-426

[17] The nondegenerate center problem and the inverse integrating factor [J].

Giné, J .

BULLETIN DES SCIENCES MATHEMATIQUES, 2006, 130 (02) :152-161

[18] A method for characterizing nilpotent centers [J].

Gine, Jaume ;

Llibre, Jaume .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 413 (01) :537-545

[19] Existence of inverse integrating factors and Lie symmetries for degenerate planar centers [J].

Gine, Jaume ;

Peralta-Salas, Daniel .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (01) :344-357

[20] NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (I) [J].

Liu, Yirong ;

Li, Jibin .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2009, 19 (11) :3791-3801

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