On the use of orbital symmetries and semi-invariants for the analysis of planar nonlinear systems

Semi-invariants can be used to study the trajectories of dynamical systems, and, in particular, to study the stability of the origin. The computation of semi-invariants can be based on orbital symmetries, which, in general, are hard to compute even for planar systems. The goal of this paper is to describe several classes of planar systems for which an orbital symmetries can be computed, and to illustrate what can be understood for such systems using the corresponding semi-invariants.