English

Generalized rational first integrals of analytic differential systems

Classical Analysis and ODEs 2014-07-31 v1 Dynamical Systems

Abstract

In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous related ones, for instance the classical Poincar\'e's one \cite{Po}, the Furta's one, part of Chen's ones, and the Shi's one. The key point in the proof of our main results is that functionally independence of generalized rational functions implies the functionally independence of their lowest order rational homogeneous terms.

Keywords

Cite

@article{arxiv.1407.7948,
  title  = {Generalized rational first integrals of analytic differential systems},
  author = {Wang Cong and Jaume Llibre and Xiang Zhang},
  journal= {arXiv preprint arXiv:1407.7948},
  year   = {2014}
}

Comments

22. Journal of Differential Equations, 2011

R2 v1 2026-06-22T05:16:23.883Z