Zero-Hopf bifurcation, periodic orbits and $C^{1}$ non-integrability of the classical Rössler system

We investigate the zero-Hopf bifurcation and the local $C^{1}$-non-integrability of the original Rössler system. First, we characterize the unique zero-Hopf equilibrium of the system and study its perturbation by means of the first-order averaging theory. We prove that, under suitable assumptions on