Higher order criterion for the nonexistence of formal first integral for nonlinear systems
Texas State University, Department of Mathematics
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.
Normal form theory, First integral, Resonance
Xu, Z., Li, W., & Shi, S. (2017). Higher order criterion for the nonexistence of formal first integral for nonlinear systems. <i>Electronic Journal of Differential Equations, 2017</i>(274), pp. 1-11.