Invariant algebraic curves and rational first integrals for planar polynomial vector fields

被引：30
|
作者：
Chavarriga, J
Llibre, J
机构：
[1] Univ Lleida, Dept Matemat, Lleida 25001, Spain
[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2001年 / 169卷 / 01期
关键词：
D O I：
10.1006/jdeq.2000.3891
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present three main results. The first two provide sufficient conditions in order that a planar polynomial vector field in C-2 has a rational first integral, and the third one studies the number of multiple points that an invariant algebraic curve of degree n of a planar polynomial vector field of degree m can have in function of m and n. (C) 2001 Academic Press.
引用
收藏
页码：1 / 16
页数：16
相关论文
共 50 条
  • [41] Symmetries of planar algebraic vector fields
    Alcazar, Juan Gerardo
    Lavicka, Miroslav
    Vrsek, Jan
    COMPUTER AIDED GEOMETRIC DESIGN, 2024, 111
  • [42] A Transfer Principle in the Real Plane from Nonsingular Algebraic Curves to Polynomial Vector Fields
    Rudolf Winkel
    Geometriae Dedicata, 2000, 79 : 101 - 108
  • [43] Algebraic invariant curves of plane polynomial differential systems
    Tsygvintsev, A
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (03): : 663 - 672
  • [44] A transfer principle in the real plane from nonsingular algebraic curves to polynomial vector fields
    Winkel, R
    GEOMETRIAE DEDICATA, 2000, 79 (01) : 101 - 108
  • [45] Polynomial Vector Fields on Algebraic Surfaces of Revolution
    Fabio Scalco Dias
    Luis Fernando Mello
    Results in Mathematics, 2021, 76
  • [46] Polynomial Vector Fields on Algebraic Surfaces of Revolution
    Dias, Fabio Scalco
    Mello, Luis Fernando
    RESULTS IN MATHEMATICS, 2021, 76 (01)
  • [47] On the number of invariant lines for polynomial vector fields
    Sokulski, J
    NONLINEARITY, 1996, 9 (02) : 479 - 485
  • [48] Characteristic integral curves of polynomial vector fields
    Brunella, M
    TOPOLOGY, 1998, 37 (06) : 1229 - 1246
  • [49] Invariant Algebraic Curves of Generalized Lienard Polynomial Differential Systems
    Gine, Jaume
    Llibre, Jaume
    MATHEMATICS, 2022, 10 (02)
  • [50] A REMARK ON FIRST INTEGRALS OF VECTOR FIELDS
    da Silva, Belotto
    Klimes, Martin
    Rebelo, Julio
    Reis, Helena
    PUBLICACIONS MATEMATIQUES, 2024, 68 (01) : 103 - 109
12345