New aspects in the unfolding of the nilpotent singularity of codimension three

摘要

This paper is concerned with three-dimensional vector fields and more specifically with the study of dynamics in unfoldings of the nilpotent singularity of codimension three. The ultimate goal is to understand the dynamic and bifurcations in the unfolding of the singularity. However, it is clear from the literature that the bifurcation diagram is very complicated and a complete study is far beyond the current possibilities, not only from a theoretical point of view but also from a numerical point of view, despite recent developments of computational methods for dynamical systems.