Higher order criterion for the nonexistence of formal first integral for nonlinear systems

Abstract

The main purpose of this article is to find a criterion for the nonexistence of formal first integrals for nonlinear systems under general resonance. An algorithm illustrates an application to a class of generalized Lokta-Volterra systems. Our result generalize the classical Poincare's nonintegrability theorem and the existing results in the literature.

Keywords

• Normal form theory
• first integral
• resonance