Starting Homoclinic Tangencies near 1:1 Resonances.

A typical problem in the numerical analysis of homoclinic orbits is the choice of an appropriate initial solution that could lead us, via e.g. Newton iterations, to the homoclinic connection we want to analyze. In this presentation we develop a theory-based numerical method for the construction of such initial solution. We concentrate on discrete-time systems of arbitrary dimension ≥ 2, having 1:1 resonances at the origin. The method relies on numerical centre manifold reduction and flow approximation. The effectiveness of the method is illustrated by numerical examples.