The Andronov–Hopf bifurcation with $2:1$ resonance

We consider dissipative dynamical systems in the neighborhood of quasi-periodic $n$-dimensional invariant tori that are not normally hyperbolic. We assume that the normal spectrum contains precisely two pairs of simple pure imaginary eigenvalues. We investigate the case where the frequencies are in the ratio $2:1$. We establish sufficient conditions for the existence of invariant tori of dimension $n+p$ in certain region of the parameter space.