Nonlinear Stability for an Anisotropic Harmonic Oscillator Coupled by a Rotating Cubic Potential

In this paper we consider a nonisotropic harmonic oscillator with Coriolis coupling, perturbed by a generalized cubic Hénon-Heiles potential. This model depends on three parameters which play an important role in the symmetry breaking of the classical Hénon-Heiles system. The main goal is to describe the equilibrium solutions of the system and their linear stability character. We also analyze the nonlinear stability of the equilibrium point at the origin, showing how the symmetry breaking, which manifests itself through the parameters of the problem, affects the stability properties through resonances.