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

页码：189 / 195

页数：7

共 50 条

[31] Darboux polynomials and first integrals of natural polynomial Hamiltonian systems
Maciejewski, AJ
Przybylska, M
PHYSICS LETTERS A, 2004, 326 (3-4) : 219 - 226
[32] Darboux integrability of the Lu system
Llibre, Jaume
Mahdi, Adam
Valls, Claudia
JOURNAL OF GEOMETRY AND PHYSICS, 2013, 63 : 118 - 128
[33] Isometric embedding and Darboux integrability
Clelland, J. N.
Ivey, T. A.
Tehseen, N.
Vassiliou, P. J.
GEOMETRIAE DEDICATA, 2019, 203 (01) : 353 - 388
[34] A Generalization of an Integrability Theorem of Darboux
Michael Benfield
Helge Kristian Jenssen
Irina A. Kogan
The Journal of Geometric Analysis, 2019, 29 : 3470 - 3493
[35] First integrals and darboux polynomials of homogeneous linear differential systems
Weil, JA
APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS AND ERROR-CORRECTING CODES, 1995, 948 : 469 - 484
[36] Darboux integrability for the Rossler system
Llibre, J
Zhang, X
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2002, 12 (02): : 421 - 428
[37] A Generalization of an Integrability Theorem of Darboux
Benfield, Michael
Jenssen, Helge Kristian
Kogan, Irina A.
JOURNAL OF GEOMETRIC ANALYSIS, 2019, 29 (04) : 3470 - 3493
[38] Isometric embedding and Darboux integrability
J. N. Clelland
T. A. Ivey
N. Tehseen
P. J. Vassiliou
Geometriae Dedicata, 2019, 203 : 353 - 388
[39] MOMENTUM MAPS, INDEPENDENT FIRST INTEGRALS AND INTEGRABILITY FOR CENTRAL POTENTIALS
Fiorani, Emanuele
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2009, 6 (08) : 1323 - 1341
[40] A note on the Darboux theory of integrability of non-autonomous polynomial differential systems
Blazquez-Sanz, David
Pantazi, Chara
NONLINEARITY, 2012, 25 (09) : 2615 - 2624

← 1 2 3 4 5 →