Search of exact invariants for PT and non-PT-symmetric complex Hamiltonian systems

We build exact dynamical invariants corresponding to PT-symmetric (Parity and Time reversal) and non-PT-symmetric complex Hamiltonian systems in two dimensions, in order to obtain an additional insight into the features of dynamical Hamiltonian systems. There are many dynamical systems which admit complex invariants and simultaneously different methods are there to obtain it. The rationalization method is used to study two-dimensional complex dynamical systems on the extended complex phase plane. The role and scope of these invariants is pointed out.