On theC1non-integrability of differential systems via periodic orbits

We go back to the results of Poincaré [Poincare, H (1891) Sur lintegration des equations differentielles du premier ordre et du premier degre I and II,Rendiconti del circolo matematico di Palermo5, 161–191] on the multipliers of a periodic orbit for proving theC1non-integrability of differential systems. We apply these results to Lorenz, Rossler and Michelson systems, among others.