Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces

Authors:	Jaume?Llibre author-information" > author-information__contact u-icon-before" > mailto:jllibre@mat.uab.es" title=" jllibre@mat.uab.es" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Xiang?Zhang

Affiliation:	(1) Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra Barcelona, Spain;(2) Department of Applied Mathematics, Shanghai Jiaotong University, 200030 Shanghai, P.R. China

Abstract:	In this paper we extend the Darboux theory of integrability in ℝⁿ to the regular algebraic hypersurfaces. Then we apply the extended theory first to the 3-dimensional generalized cylinders $(mathbb{S}^1 )$ ×ℝ^3−r of ℝ⁴ forr=0, 1, 2, 3; and after to then-dimensional sphere $mathbb{S}^n$ of ℝⁿ⁺¹.

Keywords:	KeywordHeading" > and phrases Darboux integrability generalized cylinder torus sphere
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