Integrability and Global Dynamics of Two Chaotic Systems

In this paper, integrability and the global dynamics of two chaotic systems, Coullet and Malasoma systems, are studied. We mainly use the contradiction technique to show that both systems have no polynomial, Darboux and rational first integrals. Moreover, it is proved that the Cullet system has no analytic first integrals if some conditions on the parameters are satisfied. We also give a complete description of the dynamics at infinity by Poincaré compactification technique for both aforementioned systems.