Normal resonances in a double Hopf bifurcation

We introduce a framework to systematically investigate the resonant double Hopf bifurcation. use basic invariants of ensuing T 1 -action analyse approximating normal form truncations in unified manner. In this way we obtain global description parameter space and thus find organising resonance droplet, which is present analogue gap. The dynamics yields skeleton for original system. perturbation theory both hyperbolicity (centre manifold theory) kam are being used.