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.