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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 1036089, 9 pages
http://dx.doi.org/10.1155/2016/1036089
Research Article

Formal First Integrals of General Dynamical Systems

1College of Science, Dalian Minzu University, Dalian 116600, China
2School of Mathematics, Jilin University, Changchun 130012, China

Received 22 February 2016; Accepted 4 July 2016

Academic Editor: Andrei D. Mironov

Copyright © 2016 Jia Jiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The goal of this paper is trying to make a complete study on the integrability for general analytic nonlinear systems by first integrals. We will firstly give an exhaustive discussion on analytic planar systems. Then a class of higher dimensional systems with invariant manifolds will be considered; we will develop several criteria for existence of formal integrals and give some applications to illustrate our results at last.