A procedure for the computation of semi-invariants

This paper deals with the concept of semi-invariant (Darboux polynomial), which extends to the nonlinear case the concept of eigenfunction. Semi-invariants can be used as elementary bricks for the construction of Lyapunov functions. For planar systems, the construction of semi-invariants is strictly correlated with the existence of an orbital symmetry of the system. This feature is not easily extended when the dimension of the system state is greater than 2. In this paper, a procedure is proposed that does not rely on the existence of orbital symmetries of the system, whence can be easily applied to general systems. The proposed technique is applied to some relevant and physically motivated systems.