Cooperative irreducible systems of ordinary differential equations with   first integral
  This note considers cooperative irreducible systems of ordinary differential equations admitting a $C^{1}$ first integral with positive gradient. We prove that all forward or backward nonwandering points are equilibria. We obtain also some results on the global phase portrait of such systems. The main tool of proof is a canonically defined Finsler structure with respect to which the derivative skew-product dynamical system is contractive. 
Janusz Mierczy\'nski
math.CA math.DS