On the cyclicity of weight-homogeneous centers

被引：19

作者：

Gavrilov, Lubomir ^{[2
]}

Gine, Jaume ^{[1
]}

Grau, Maite ^{[1
]}

机构：

[1] Univ Lleida, Dept Matemat, Lleida 25001, Spain

[2] Univ Toulouse, Inst Math, UMR 5219, F-31062 Toulouse 9, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 246卷 / 08期

关键词：

Weight-homogeneous differential system; Poincare-Pontryagin-Melnikov function; Cyclicity; Nilpotent center; Inverse integrating factor; VECTOR-FIELDS; LIMIT-CYCLES;

D O I：

10.1016/j.jde.2009.02.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let W be a weight-homogeneous planar polynomial differential system with a center. We find an upper bound of the number of limit cycles which bifurcate from the period annulus of W under a generic polynomial perturbation. We apply this result to a particular family of planar polynomial systems having a nilpotent center without meromorphic first integral. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：3126 / 3135

页数：10

共 11 条

[1]

Andreev A., 1958, Trans. Amer. Math. Soc, V8, P187

[2] Successive derivatives of a first return map, application to the study of quadratic vector fields [J].

Francoise, JP .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1996, 16 :87-96

[3]

GAVRILOV L, 2005, ANN FAC SCI TOULOUSE, V14, P663

[4] On second order bifurcations of limit cycles [J].

Iliev, ID .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1998, 58 :353-366

[5]

Ilyashenko Y., 1969, MAT SBORNIK, V78, P360

[6]

LI C, 2001, EXTRACTA MATH, V16, P441

[7] Limit Cycles Bifurcating from the Period Annulus of Quasi-Homogeneous Centers [J].

Li, Weigu ;

Llibre, Jaume ;

Yang, Jiazhong ;

Zhang, Zhifen .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2009, 21 (01) :133-152

[8]

Llibre J, 2001, DYNAM CONT DIS SER A, V8, P161

[9]

Perko L., 2001, Differential Equations and Dynamical Systems, Vthird, DOI DOI 10.1007/978-1-4613-0003-8

[10]

Spivak M.D., 1970, A comprehensive introduction to differential geometry

← 1 2 →