Complex Invariants Corresponding Non-hermitian \(\mathcal{P}\mathcal{T}\) -Symmetric Hamiltonian

In this work, we build exact dynamical invariants for complex Hamiltonian systems. Our aim is to extract an further understanding into the aspects of a dynamical system, we build here complex dynamical invariant. There could be systems which may concede complex invariants. To accomplish this we adopt rationalization formalism to analyse complex dynamical systems on the continued complex phase plane. Scope and purview of attained invariant is acuminated.