Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2

被引：27
|
作者：
Cairo, Laurent
Llibre, Jaurne [1 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain
[2] Univ Orleans, MAPMO CNRS, Dept Math, F-45067 Orleans 2, France
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 67卷 / 02期
关键词：
quadratic vector fields; integrability; rational first integral; phase portraits;
D O I：
10.1016/j.na.2006.04.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector field there are exactly 25 different global phase portraits in the Poincare disc, up to a reversal of sense. (c) 2006 Elsevier Ltd. All rights reserved.
引用
收藏
页码：327 / 348
页数：22
相关论文
共 50 条
  • [1] Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3
    Llibre, Jaume
    Oliveira, Regilene D. S.
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (10) : 3549 - 3560
  • [2] Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3 (vol 70, pg 3549, 2009)
    Llibre, Jaume
    Oliveira, Regilene D. S.
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) : 6378 - 6379
  • [3] PHASE PORTRAITS AND INVARIANT STRAIGHT LINES OF CUBIC POLYNOMIAL VECTOR FIELDS HAVING A QUADRATIC RATIONAL FIRST INTEGRAL
    Llibre, Jaume
    Mahdi, Adam
    Vulpe, Nicolae
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2011, 41 (05) : 1585 - 1629
  • [4] Phase portraits of the quadratic vector fields with a polynomial first integral
    García B.
    Pérez Del Río J.S.
    Llibre J.
    Rendiconti del Circolo Matematico di Palermo, 2006, 55 (3) : 420 - 440
  • [5] Phase portraits of cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2
    Cairo, Laurent
    Llibre, Jaume
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2007, 40 (24) : 6329 - 6348
  • [6] Phase portraits for quadratic homogeneous polynomial vector fields on S-2
    Llibre, Jaume
    Pessoa, Claudio
    RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2009, 58 (03) : 361 - 406
  • [7] Polynomial first integrals of quadratic vector fields
    Chavarriga, Javier
    Garcia, Belen
    Llibre, Jaume
    Perez del Rio, Jesus S.
    Rodriguez, Jose Angel
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 230 (02) : 393 - 421
  • [8] Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems
    Garcia, Belen
    Giacomini, Hector
    Perez del Rio, Jesus S.
    APPLIED MATHEMATICS LETTERS, 2011, 24 (07) : 1115 - 1119
  • [9] A class of polynomial planar vector fields with polynomial first integral
    Ferragut, A.
    Galindo, C.
    Monserrat, F.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 430 (01) : 354 - 380
  • [10] Phase portraits of a new class of integrable quadratic vector fields
    Llibre, J
    del Río, JSP
    Rodríguez, JA
    DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS, 2000, 7 (04): : 595 - 616
12345