Varieties of local integrability of analytic differential systems and their applications

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:257

Article

Romanoyski, Valery G.^1,2  Xia, Yonghui³  Zhang, Xiang^4,5 

[1] Univ Maribon, Ctr Appl Math & Theoret Phys, SI-2000 Maribor, Slovenia

[2] Univ Maribon, Fac Nat Sci & Math, SI-2000 Maribor, Slovenia

[3] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[4] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[5] Shanghai Jiao Tong Univ, MOE LSC, Shanghai 200240, Peoples R China

关键词: Analytic differential systems;    Local integrability;    Variety;    Hamiltonian system;    Darboux integrability;   

DOI  :  10.1016/j.jde.2014.06.007

来源: Elsevier

【 摘 要 】

In this paper we provide a characterization of local integrability for analytic or formal differential systems in R-n or C-n via the integrability varieties. Our result generalizes the classical one of Poincare and Lyapunov on local integrability of planar analytic differential systems to any finitely dimensional analytic differential systems. As an application of our theory we study the integrability of a family of four-dimensional quadratic Hamiltonian systems. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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