Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces

Jaume Llibre; Xiang Zhang

doi:https://doi.org/10.1007/BF02871455

Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces

Jaume Llibre, Xiang Zhang

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

17 Citations (Scopus)

Abstract

In this paper we extend the Darboux theory of integrability in ℝ n to the regular algebraic hypersurfaces. Then we apply the extended theory first to the 3-dimensional generalized cylinders (S 1) × ℝ 3-r of ℝ 4 for r=0, 1, 2, 3; and after to then-dimensional sphere S n of ℝ n+1. © 2002 Springer.

Original language	English
Pages (from-to)	109-126
Journal	Rendiconti del Circolo Matematico di Palermo
Volume	51
DOIs	https://doi.org/10.1007/BF02871455
Publication status	Published - 1 Feb 2002

Keywords

Darboux integrability
generalized cylinder
sphere
torus

Access to Document

https://doi.org/10.1007/BF02871455

Cite this

@article{470c707736dc4f8788bd95772ca284e2,

title = "Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces",

abstract = "In this paper we extend the Darboux theory of integrability in ℝ n to the regular algebraic hypersurfaces. Then we apply the extended theory first to the 3-dimensional generalized cylinders (S 1) × ℝ 3-r of ℝ 4 for r=0, 1, 2, 3; and after to then-dimensional sphere S n of ℝ n+1. {\textcopyright} 2002 Springer.",

keywords = "Darboux integrability, generalized cylinder, sphere, torus",

author = "Jaume Llibre and Xiang Zhang",

year = "2002",

month = feb,

day = "1",

doi = "https://doi.org/10.1007/BF02871455",

language = "English",

volume = "51",

pages = "109--126",

}

TY - JOUR

T1 - Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces

AU - Llibre, Jaume

AU - Zhang, Xiang

PY - 2002/2/1

Y1 - 2002/2/1

N2 - In this paper we extend the Darboux theory of integrability in ℝ n to the regular algebraic hypersurfaces. Then we apply the extended theory first to the 3-dimensional generalized cylinders (S 1) × ℝ 3-r of ℝ 4 for r=0, 1, 2, 3; and after to then-dimensional sphere S n of ℝ n+1. © 2002 Springer.

AB - In this paper we extend the Darboux theory of integrability in ℝ n to the regular algebraic hypersurfaces. Then we apply the extended theory first to the 3-dimensional generalized cylinders (S 1) × ℝ 3-r of ℝ 4 for r=0, 1, 2, 3; and after to then-dimensional sphere S n of ℝ n+1. © 2002 Springer.

KW - Darboux integrability

KW - generalized cylinder

KW - sphere

KW - torus

U2 - https://doi.org/10.1007/BF02871455

DO - https://doi.org/10.1007/BF02871455

M3 - Article

VL - 51

SP - 109

EP - 126

ER -

Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces

Abstract

Keywords

Access to Document

Fingerprint

Cite this