GLOBAL SOLUTIONS TO INVOLUTIVE SYSTEMS

被引：10

作者：

Bergamasco, A. P. ^{[1
]}

Kirilov, A. ^{[2
]}

Nunes, W. V. L. ^{[1
]}

Zani, S. L. ^{[1
]}

机构：

[1] ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil

[2] UFPR, Dept Matemat, BR-81531980 Curitiba, Parana, Brazil

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 143卷 / 11期

基金：

巴西圣保罗研究基金会;

关键词：

Global solvability; complex; 1-form; periodic solutions; OVERDETERMINED SYSTEMS; SOLVABILITY; COMPLEX;

D O I：

10.1090/proc/12633

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we consider a class of systems of two vector fields on the 3-torus associated to a closed smooth complex 1-form c = a + ib with b exact. Necessary conditions and sufficient conditions for this system to be globally solvable are provided in terms of the position of the global extrema and the connectedness of sublevel and superlevel sets of the primitives of b, together with arithmetical properties of the periods of a.

引用

页码：4851 / 4862

页数：12

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