ON SYMMETRY AND INVARIANT OF DYNAMICAL SYSTEMS

In this paper, we review the research results published in recent ten years on symmetry and invariant of dynamical systems, including generalized Noether symmetries, higher-order Noether symmetries, Lie symmetries, pseudo-symmetries and adjoint symmetries. We also present here for the first time our research results on higher-order Noether symmetries and Lic symmetries for nonconscrvative dynamical systems.