On the period function of x"+f(x)x′2+g(x)=0

被引：60

作者：

Sabatini, M ^{[1
]}

机构：

[1] Univ Trent, Dipartimento Matemat, Trent, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2004年 / 196卷 / 01期

关键词：

center; period function; monotonicity; polynomial systems;

D O I：

10.1016/S0022-0396(03)00067-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the period function T of a center O of the title's equation. A sufficient condition for the monotonicity of T, or for the isochronicity of O, is given. Such a condition is also necessary, when f and g are odd and analytic. In this case a characterization of isochronous centers is given. Some classes of plane systems equivalent to such equation are considered, including some Kukles' systems. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：151 / 168

页数：18

共 14 条

[1] Isochronicity via normal form [J].

Algaba A. ;

Freire E. ;

Gamero E. .

Qualitative Theory of Dynamical Systems, 2000, 1 (2) :133-156

[2]

Chavarriga J., 1999, QUAL THEORY DYN SYST, V1, P1, DOI DOI 10.1007/BF02969404

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

CHICONE, C .

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

[4]

CHOUIKHA R, 1999, APPL MATH, V26, P243

[5]

CHOW SN, 1986, CASOPIS PEST MAT, V11, P14

[6]

CHRISTOPHER CJ, 1998, CLASSIFICATION LIENA

[7] Period function for a class of Hamiltonian systems [J].

Cima, A ;

Gasull, A ;

Mañosas, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 168 (01) :180-199

[8]

FREIRE E, 2001, 1 DERIVATIVE PERIOD

[9]

Jacobson N., 1974, BASIC ALGEBRA, VI

[10]

MAZZI L, 2000, REND MAT ACCAD LINCE, V11, P81

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