On orbital-reversibility for a class of planar dynamical systems

•We study if a planar system admits hidden nonlinear involutory reversing symmetries.•We determine if the system admits some reversibility by reparametrizing the time.•Our study uses some properties of invariant curves of the system.•The results are applied to some nilpotent and degenerate families of systems.

We give necessary conditions for the orbital-reversibility for a class of planar dynamical systems, based on properties of some invariant curves. From these necessary conditions we formulate a suitable algorithm, to detect orbital-reversibility, which is applied to a family of nilpotent systems and to a family of degenerate systems.