On the number of critical periods for planar polynomial systems

被引：26

作者：

Cima, Anna ^{[1
]}

Gasull, Armengol ^{[1
]}

da Silva, Paulo R. ^{[2
]}

机构：

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

[2] IBILCE UNESP, BR-15054000 Sao Paulo, Brazil

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 07期

基金：

巴西圣保罗研究基金会;

关键词：

period function; critical periods; perturbations; potential systems; reversible centers; Hamiltonian centers; Lienard centers;

D O I：

10.1016/j.na.2007.07.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree l with at least 2[(l - 2)/2] critical periods as well as study concrete families of potential, reversible and Lienard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not. increases with the order of the perturbation. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：1889 / 1903

页数：15

共 16 条

[1] THE MONOTONICITY OF THE PERIOD FUNCTION FOR PLANAR HAMILTONIAN VECTOR-FIELDS [J].

CHICONE, C .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1987, 69 (03) :310-321

[2] FINITENESS FOR CRITICAL PERIODS OF PLANAR ANALYTIC VECTOR-FIELDS [J].

CHICONE, C ;

DUMORTIER, F .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 20 (04) :315-335

[3]

CHICONE C, 1998, T AM MATH SOC, V102, P706

[4]

CHICONE C, MATH SCI NET

[5] POLYNOMIAL SYSTEMS - A LOWER-BOUND FOR THE HILBERT-NUMBERS [J].

CHRISTOPHER, CJ ;

LLOYD, NG .

PROCEEDINGS OF THE ROYAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1995, 450 (1938) :219-224

[6] Algebraic properties of the Liapunov and period constants [J].

Cima, A ;

Gasull, A ;

Manosa, V ;

Manosas, F .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1997, 27 (02) :471-501

[7]

Collins C., 1996, DIFFER INTEGRAL EQU, V9, P251

[8]

Coppel W. A., 1993, DIFFER INTEGRAL EQU, V6, P1357

[9] The period function of classical Lienard equations [J].

De Maesschalck, P. ;

Dumortier, F. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 233 (02) :380-403

[10] The successive derivatives of the period function of a plane vector field [J].

Francoise, JP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 146 (02) :320-335

← 1 2 →