Limit cycles bifurcating from a perturbed quartic center

被引：24

作者：

Coll, Bartomeu ^{[1
]}

Llibre, Jaume ^{[2
]}

Prohens, Rafel ^{[1
]}

机构：

[1] Univ Illes Balears, Dept Matemat & Informat, Fac Ciencies, Palma de Mallorca 07071, Spain

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

来源：

CHAOS SOLITONS & FRACTALS | 2011年 / 44卷 / 4-5期

关键词：

HAMILTONIAN CENTERS; GLOBAL BIFURCATION; SYSTEMS; NUMBER; FAMILY; SHAPE;

D O I：

10.1016/j.chaos.2011.02.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the quartic center (x) over dot = -yf (x, y), (y) over dot = xf (x, y), with f(x,y)= (x + a) (y + b) (x + c) and abc not equal 0. Here we study the maximum number a of limit cycles which can bifurcate from the periodic orbits of this quartic center when we perturb it inside the class of polynomial vector fields of degree a, using the averaging theory of first order. We prove that 4[(n - 1)/2]+4 <= sigma <= 5[(n - 1)/2] + 14, where [eta] denotes the integer part function of eta. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：317 / 334

页数：18

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