Formal First Integrals of General Dynamical Systems

Abstract EN

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.