Varieties of local integrability of analytic differential systems and their applications

Valery G Romanovski,Xiang Zhang,Yonghui Xia

doi:10.1016/j.jde.2014.06.007

Varieties of local integrability of analytic differential systems and their applications

Valery G Romanovski, Xiang Zhang + Show 1 more

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https://doi.org/10.1016/j.jde.2014.06.007

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Journal: Journal of Differential Equations	Publication Date: Jun 18, 2014
Citations: 23	License type: publisher-specific-oa

Affiliation: University of Maribor, Shanghai Jiao Tong University, Zhejiang Normal University

#Analytic Differential Systems #Analytic Systems + Show 8 more

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Abstract

In this paper we provide a characterization of local integrability for analytic or formal differential systems in Rn or Cn via the integrability varieties. Our result generalizes the classical one of Poincaré 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.

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