Numerical investigation of Poincare resonances

In accordance with Prigozhin there are two reasons for dynamic systems stability breakdown, and their numerical integration impossibility on wide time frames - trajectories stirring and Poincare resonance. On the one hand trajectories stirring is a result of numerical integration, on the other hand Poincare resonances are polynomials generating normal form that can be obtained before numerical integration. Thus these two reasons have rather different natures. Hence, the following question arises - can we say something about existence of strange attractor in dynamic systems before their numerical or analytical integration? We investigate this question in the terminology of dynamic system Poincare normal forms.