Rational first integrals in the Darboux theory of integrability in Cn

被引：42
|
作者：
Llibre, Jaume [1 ]
Zhang, Xiang [2 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2010年 / 134卷 / 02期
关键词：
Darboux integrability; Rational first integral; EQUATIONS;
D O I：
10.1016/j.bulsci.2007.12.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In 1979 Jouanolou showed that if the number of invariant algebraic hypersurfaces of a polynomial vector field in R-n or C-n of degree d is at least ((d+n-1)(n)) + n, then the vector field has a rational first integral. His proof used sophisticated tools of algebraic geometry. We provide an easy and elementary proof of Jouanolou's result using linear algebra. (C) 2007 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：189 / 195
页数：7
相关论文
共 50 条
  • [21] Darboux theory of integrability on the Clifford n-dimensional torus
    Llibre, Jaume
    Valls, Claudia
    BULLETIN DES SCIENCES MATHEMATIQUES, 2024, 192
  • [22] A Darboux-type theory of integrability for discrete dynamical systems
    Gasull, A
    Mañosa, V
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2002, 8 (12) : 1171 - 1191
  • [23] Darboux polynomials and first integrals of polynomial Hamiltonian systems
    Pranevich, Andrei
    Grin, Alexander
    Musafirov, Eduard
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2022, 109
  • [24] First integrals of a generalized Darboux-Halphen system
    Chakravarty, S
    Halburd, R
    JOURNAL OF MATHEMATICAL PHYSICS, 2003, 44 (04) : 1751 - 1762
  • [25] Geometry, integrability and bifurcation diagrams of a family of quadratic differential systems as application of the Darboux theory of integrability
    Oliveira, Regilene
    Schlomiuk, Dana
    Travaglini, Ana Maria
    Valls, Claudia
    ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2021, (45) : 1 - 90
  • [26] Rational first integrals for periodic systems
    Jiao, Jia
    Shi, Shaoyun
    Zhou, Qingjian
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2011, 62 (02): : 233 - 243
  • [27] Rational first integrals for periodic systems
    Jia Jiao
    Shaoyun Shi
    Qingjian Zhou
    Zeitschrift für angewandte Mathematik und Physik, 2011, 62 : 233 - 243
  • [28] First integrals and Darboux polynomials of natural polynomial Hamiltonian systems
    Garcia, Isaac A.
    Grau, Maite
    Llibre, Jaume
    PHYSICS LETTERS A, 2010, 374 (47) : 4746 - 4748
  • [29] Theory of log-rational integrals
    Crandall, Richard E.
    GEMS IN EXPERIMENTAL MATHEMATICS, 2010, 517 : 127 - 142
  • [30] Darboux linearization and isochronous centers with a rational first integral
    Mardesic, P
    MoserJauslin, L
    Rousseau, C
    JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 134 (02) : 216 - 268
12345