Starting homoclinic tangencies near 1:1 resonances

Abstract

In  this  presentation  we  construct  a  theory-based  numericalmethod  for  starting  the  continuation  of  homoclinic  tangenciasnear 1 : 1 resonances, for systems with arbitrary dimension ≥ 2. The method is based on numerical center manifold reduction and flow approximation. The effectiveness of the method is illustrated by numerical examples.